Chapter

Refraction of Light (B) Light

4 at Plane Surfaces
SYLLABUS

i) Retraction of light through a glass block and a triangular prism, qualitative treatment of simple applications
such as real and apparent depth of objects in water and apparent bending of sticks in water. ApplicationS of
refraction of light.
Sonne of syllabus : Partial reflection and refraction due to change in medium. Laws of refraction, the effect on
ened (V), wavelength (2) and frequency () due to refraction of light, conditions for a light ray to pass undeviated.
Valnes of speed of light (c) in vacuum, air, water and glass; refractive index u = cNV=f. Values of p for
common substances such as water, glass and diamond, experimental verification; refraction through glass block;
lateral displacement; multiple images in thick glass plate/mirror; refraction through a glass prism; simple
anplications: real and apparent depth of objects in water; apparent bending of a stick under water. (Simple
numerical problems and approximate ray diagrams required.)
Gi) Total internal reflection; Critical angle; examples in triangular glass prisms; comparison with reflection from
a plane mirror (qualitative only). Applications of total intermal reflection. XX
Scope of syllabus : Transmission of light from a denser medium (glass/water) to a rarer medium (air) at different
angles of incidence; critical angle C, 4 = /sin C. Essential conditions for total internal reflection. Total intermal
reflection in atriangular glass prism; ray diagram, different cases - angles of prism (60°, 60°, 60°), (60°, 309, 90°),
(45°, 45°, 90°); use of right angle prism to obtain &= 90° and 180° (ray diagram); comparison of total internal
reflection from a prism and reflection from a plane mirror.

(A) REFRACTION, LAWS OF REFRACTION AND REFRACTIVE INDEX

In classIX, we have read about reflection of While passing fromn one medium to the other,
light from plane and spherical mirrors. The return f light slows down, the second medium is said
of light in the same medium after striking a to be optically denser* than the first medium and
polished surface is called reflection of light. f light speeds up, the second medium is said to
be optically rarer than the first medium. Thus,
Reflection of a light ray obeys two laws : (i)) the
angle of reflection is equal to the angle of water and glass are optically denser than air (or
air is optically rarer than water and glass).
incidence, and (iiY the incident ray, the normatat
the point of incidence and the reflected ray, allSimilarly, glass is optically denser than water (or
lie in one plane) Here we shall study refraction water is optically rarer than glass).
of light through plane and spherical surfaces of 4.1 REFRACTION OF LIGHT
ransparent media. Partial reflection and refraction at the
Light has the maximum speed (= 3 x 10 ms) boundary of two different media : In a
in vacuum and it travels with different speeds transparent homogeneous medium light travels with
in different media, It travels faster in air a constant speed in a straight line path, but when
Ihan in water or in glass. The speed of light is * Optical density has no relationwith the density of medium. Kerusene
3 x10 m s in air, 2:25 x 108ms in water_and is less dense than water (as it floats on water), but it is optically denser
than water. Optical density of a medium depends on the seed oe
X10 ms in glass, Light travels at a constant light in that medium, while the density of a mediun derends oa its
Specd in a transparent homogeneous medium. inter-molecular separation.
75
 transparent medium
a ray of light travelling in one
A

another
strikes obliquely at the surface of
transparent mediunm, a part of light goes back to VCID EC

reflection
the same medium obeying the laws of AIR (RARER) MEDIUM 1
and is called the reflected light. The remaining part
travels
GLASS MEDIUM 2
of light enters into the other medium and
(DENSER)

in a sraight path but in a direction different from

its iniial direction and is called the refracted light.
Thus, at the boundary separating the tvo M TED
media, light suffers partial reflection and partial Fig. 4.1 Refraction from rarer to denser medium
refraction. (2) When a ray of light travels from,
The change in thedirection of the path of light, denser medium to ararer medium (say, fron
when o passes fron oue transparent medium glass to air), it bends away from the normal (ie
to another transparent medium, is called Zr> Zi) as shown in Fig. 4.2. The deviation
refraction The nefraction of light is essentially the ray is then Ó=r-i.
asurface phenomnERon.
A

In Fig. 4.1 and Fig. 4.2, SS' is the surface

separating the two media (say, air and glass). When
light travelling in medium 1 falls on the surface SS, GLASS INCDE
(DENSER) MEDIUM 1

a small part of it is reflected back in the same AIR (RARER)

MEDIUM 2

medium obeying the laws of reflection and the rest

of it is refracted through the boundary into
medium 2 ie, there is partial reflection and partial
refraction a the bondary surface. The intensity (or M
REFRACATEY CTED
the amplitude) of the refracted light will be less than Fig. 4.2 Refraction from denser to rarer medium
that of the incident light because a part of the (3) The ray of light incident normally on the
incident light's intensity has been lost by reflection. Surface separating the two media, passes
In Fig. 4.1 and 4.2, for the incident ray AO, undeviated (i.e., such a ray suffers no bending at
the refracted ray is OB, the reflected ray is OC, the surface). Thus, in case of light incident
and the normal at the point of incidence O is normally i.e. when angle of incidence Zi =0:
NOM. The angle which the incident ray makes then angle of refraction Zr= 0° as shown in Fig
with the normal, i.e. the angle of incidence i is 4.3. The deviation of the ray is zero (i.e., ð =0)
ZAON and the angle which the refracted ray A
INCIDENT

makes with the normal, i.e. the angle of refraction RAY

r is B0M. Note that angle r is not equal to

angle i (i.e., ray OB is not in the direction of OA). Zi= 0° 90
AIR (RARER) MEDIUM 1
It has been experimentally observed that GLASS OR O MEDIUM2
WATER Lr= 0°
(1) When aray of light travels from a (DENSER)
rarer medium to a denser medium (say, from REFRACTEDS
air to glass), it bends towards the normal (i.e., B
RAY
Lr < Li) as shown in Fig. 4.1. The deviation* Fig. 4.3 Refraction at normal incidence
of the ray (from its initial path) is &= i-r. onward,
Note : In discussing refraction now surface
* Deviation means the angle through which the ray turns i.e. the
angle betveen the direction of refracted ray and the direction of the reflected ray from the boundary there.
incident ray It isdenoted by the letter &. will not be shown although it is always
76
 refraction (or cause of change in Unit : The refractive index has no unit as it
Cause of
direction) hot kik is the ratio of two similar quantities.
When
ray of light passes from one medium Effect on speed (V, frequency ( ) and
another medium, its direction (or path) wavelength (2) due to refraction
of light
to of the change in speed of light When a ray of light gets refracted from a rarer
changes because medium to
from one another. In passing to a denser medium, the speed of light
in going medium to another, if light slows down. decreases; while if it is refracted from a denser
from one to a rarer medium, the speed of light increases.
bends towards the normal and if light
it away from the normal. If the 2.
speeds up, it bends The frequency f of light does not change on
remains the same in passing from refraction as it depends on the souTce of light.
speed of light
to another, the ray of light does not 3. The wavelength changes on refraction. The
one medium undeviated.
bend. It passes speed of light Vin a medium is related to
incidence (Zi = 0°) the frequency f and its wavelength à(in that
Note : In case of normal
medium to another. medium), as :
for light passing from one direction of
the speed of light changes but the V=f
light does not change.
or wavelength = ...(4.2)
REFRACTION
4.2 LAWS OF
Refraction of light obeys two laws of When light passes from a rarer to a denser
refraction which were given by the Dutch scientist medium, the wavelength decreases(since
Willebrod Snell, So they are known as Snell's speed of light decreases. but its requency
laws after his name. They are : remains unchanged).
(The incident ray, the refracted ray and the When light passes from a denser medium to
normal at the point of incidence, all lie in a rarer mnedium, its wavelength increases as
she same plane. the speed of light increases.
A2) The ratio of the sine of the angle of Note : The relationship between wavelengths
incidence i to the sine of the angle of in two media is given ahead.
refraction r is constant for the pair of given 4.3 SPEEDOF LIGHT IN DIFFERENT MEDIA;
media. i.e., mathematically RELATIONSHIP BETWEEN REFRACTIVE
ieio sini INDEX AND SPEED OF LIGHT ( = c/)
Sin r
= Constant H .(4.1) The speed of light is marimum in vacuum and
is equal to 3x 10 m s*. The speed of light in
The constant ,H, is called the refractive index air is nearly the same as in vacuum. It is denoted
of the second medium with respect to the first by the symbol c. In any other transparent media, the
medium. Here the Greek letter u (mew) is speed of ight is less than that in air (or vacuum).
the symbol used for refractive index. The refractive index of a medium is generally
Refractive index defined with respect to vacuum (or air), and is
The refractive index of second medium with called the absolute refractive index (or simply the
respect to the first medium is defined as Ihe refracive index) of the medium. It is denoted by
the letter .
ratio of the sine of the angle of incidence in
the first medium to the(sine of the The refractive index of a medium is defined
angle of. as the ratio of the speed of light in vacuum
refraction) in the second medium.
Precisely the speed of ight in vacuum is 299,792,458 ms.
77
(or air) to the speed of light in that meduum,_ related to the spced of light in the two med:
follows :
i.e.,
Speed of ight in vacuum or air (c) Speed of light in medium 1
..(4.3) Speed of light in medium 2
Speed of light in that medium (V) (4.4)
The refractive index of a transparent medium
Where represents the
1.
refractive index
always greater than 1 (it can not be less medium 2 with respect to medium
is
than 1), because speed of light in any medium is If V, is the speed of light in medium 1and V, is
(42
always less than that in vacuum (i.e., V< c). the speed of light in medium 2, then from egn.
Obviously u = 1 for air or vacuum.
Exanmples : (1) The speed of light in air is chu, (45)
3x 10 ms and in glass it is 2 x 108 m :
therefore the refractive index of glass is Here 4, and u, are the absolute refractive indices
3x10 of medium l and 2 respectively.
= 1:5 Examples : (1) Refractive index of glass with
au glass 2x10
respect to water is
(2) The speed of light in water is Speed of light in water
2.25 x 10$ m s, so the refractive index of water glas
water is
Speed of light in glasseWAL SA
2.25 × 108
3x10 4
25vIns==l33 2.0 x 108 = 1-125 otote
awer oiots
Pglass 3/2 = 1-125dolliW
or waterglass water
(3) The refractive index of dianmond is 2.41. 4/3
It means that light travels in air 2-41 times faster (2) Refractive index of water with respect to
than in diamond, or speed of light in diamond is glass is
Speed of light in glass
41 times the speed of light in ai- The speed glasswater Speed of light in water
of light in air is 3 x 10 ms, the speed of light 2-0x 108
=0-89s
in diamond is 1-245 x 10 m -!. 2-25 x 10
The refractive indices of some common water 4/3
or glasswater 3/2 = 0-89
transparent substancs ae given in the table below. Bglass

Refractive indice ig) of some common substances Note : If the refractive indices of medium 1
Suhstane Substance and medium 2 are the same, the speed of light
Vacuua Paraffin oil 1-44
will be the same in both the media, so a ray
Air 10 Glycerine 1-47
of light will pass from medium 1to medium
(003) Turpentine oil 1-47 2 without any change in its path even when
ke 131 Ordinary glass 1:5 the angle of incidence in medium 1 is not zero.
Water 1-33 Crown glass 1-53
Methylated
spurit 1-36
Quartz
Rock salt
1-54
1-56
Conditions for a light ray to pass undeviated
on refraction
Ether I-36 Carbon disulphide 1-63
Alcohol 1-37 Flint glas 1-65 A ray of light passes undeviated from
Kerosene 141
medium 1to medium 2 in either of the following
Ruby 1-76
Sulphunc acid I-43 Diamond wo conditions :
241
(1) When the angle of incidence at the
In general, the refractive index of second boundary of two mediais zero (i.e.,
medium with respect to first medium is i=0° so r= 0) as shown in Fig. 4.3.
78
 (2) When the refractive index of medium 2 Physical condition such as temperature :
is same as that of medium I (Fig. 4.4)
With increase in temperature, the refractive
i.e., u, = , i=r. index of the medium decreases. So, the speed
A of light in the medium increases.
(3 The colour or wavelength of light : The
S speed of light of all the colours is the same
in air (or vacuum), but in any other
transparent medium, the speed of light is
B
different for different colours. In a given
medium, the speed of red light is maximum
Fig. 4.4 No deviation if,=H, =p (say) and that of the violet light is Jeast, therefore
Relationship between wavelength in the two the refractive indeI of that medium is
medium y maximum for violet light and least for red
If a ray of light of frequency_f and light (i.e.. Hy > H). The wavelength of
visible light increases from the violet to the
wavelength suffers refraction from air (speed of red end, so refractive index of a medium
light = c) to a medium in which the speed of decreases with the increase in wavetength.
light is V, then the frequency of light in the
medium remains unchanged (equal to , but the 4.4 PRINCIPLE OF REVERSIBILITY OF
of light changes to 1 such that in air
wavelength THE PATH OF LIGHT
and in medium f= According to this principle, the path ef a light
C
ray is reversible.
0r '=
In Fig. 4.5, a ray of light AO is incident at
But
C
= u the refractive index of the medium. an angle ion a plane surface SS´ separating the
V two media 1 and 2. It is refracted along OB at
N= (4.6) an angle of refraction r. The refractive index of
medium 2 with respect to medium I is
Obviously when light passes from a rarer to a sini
P2 sinr . . (i)
denser medium (u > 1), its wavelength decreases
(a <2), but if light passes from a denser to a
rarer medium (4 < 1), its wavelength increases
(N> 2).
MEDUM
Factors affecting the refractive index of a MEDIUNM2
medium
The refractive index of a medium depends on
the following three factors
Nature of the medium (on the basis of Fig. 45 Principle of reversibility
Dspeed of light) : Less the speed of light
7F in a medium as compared to that in air, Now, if refraction takes place from medium
more is the refractive index of the medium 2 to 1, the prìnciple of reversibility requires that
C the ray of light incident along BO at 0 at an
(H= angle of incidence r in mnedium 2 will get
glass = 2 x 108 m s, Helass = 1-5 and refracted only along OA at an angle of refraction
water - 2-25 x 108 m s, Ler 1-33. iin medium l and in no other direction than OA.
79
 The refractive index of medium I with respect to (7) Then remove the pins one by
medium 2 is then marking a dot at the position of eachone afte
sinr afine pencil. Remove the block and pin with
sini .. (ii) line BC
points cand dby a join tie
which
boundary line RS at a point B. Join meets the
Oand Bby a straight line which the
From eqns. () and (i),
sini sin pointhtse
gives
X
sini path of light ray inside the glass block
Here AO represents the incident ray, OB .
.. (4.7) refracted ray through the glass block and Re
the emergent ray. NOM is the glass norma
1
at the point of incidence O, ZAON is
Or or ¡2= 2H1 . (4.8) angle of incidence i and ZBOM is the angle
of refraction r
Thus, if refractive index of glass with respect
3 A N
to air is H, = , the refractive1 index of air with
2
respect to glass will be=3 =7
4.5 EXPERIMENTAL VERIFICATION OF P Q

LAWS OF REFRACTION AND GA

DETERMINATION OF REFRACTIVE
INDEX OF GLASS GLASS BLOCK
S
Procedure : B
c
(1) Place a rectangular glass block on a white
o1sheet af paper fixed on a drawing board and
36 draw its, boundary line PQRS with a pencil
as shown in Fig. 4.6. Fig. 4.6 Verfication of laws of refraction
(2) Remove the block and on the boundary line (8)
Measure the angles iand r. Read the values
PQ, take a point Onearly at its middle and of sin i and sin from the sine table and
then draw a normal NOM on the line PQ
the point 0. atcalculate the ratio\sin ilsin r. This ratio is
constant and it give_ the refractive index of
(3) Draw a line AO inclined at an angle i (say, glass.
40°) to the normal NOM.
Alternative method : In order to verfiy the
(4) Replace the glass block exactly on its law of refraction without masuring the angles i
boundary line. and r, draw a circle of suitable radius with the point
(5) Fix two pins aand b Oas centre which intersects the incident ray A0 at
verticatly on tne board, Dand the
about 5 cm apart, on the line AO. refracted ray OB at E. Draw nomas
DF and EG on NOM from the points D and E
(6) Now looking from the other sidè RS of the respectively. Measure the length of the nomals Dr
block by keeping the eye close to the plane and EG with the helo of a scale. Find DF/EG Thns
of the board, fix two more pins c and d such
ratio is constant and it gives the refractive nde
that the base of all the four pins a, b, C and
of glass. This can be seen as follows :
d appear to be in a straight line as seen
DF
through the block. In right-angled AOFD, sin i= OD

80
 ad in right-angled AOGE,
sinrs EG
normal NOM. It travels inside the glass in a
OE
DF/OD Straight path along OB. At the surface RS. the ray
sin r EG/OE OB suffers another refraction. N,BM, is the
But OD =(OE, being the radi of the same circle. nomal to the surface RS at point of incidence
the
DF B. The ray OB now enters from glass (denser
EG medium) to air (rarer medium), so it speeds up
(9) Repeat the steps (3) to (8) of the experiment and bends away from the normal NBM, It
or difterent values of angle of incidence i travels along BC in air. The ray AO is called the
the
equalto 50°, 60, 70°, S0° and in each case, incident ray, OB the refracted ray and BC
sin i DF emergent ray. ZAON is the angle of incidence i,
hnd the ratio sin r or EG BOM is the angle of refraction r and ZCBM,
Reecord your observations in the table shown 1S the angle of emergence e. Since refraction
(10) occurs at two parallel surfaces PQ and RS,
below
sin i DF
therefore, MOB = N,BO and by the principle
Sin i Sin r
SN. Sin r
or
EG of reversibility of the path of a light ray
or DFor EG
Le = i i.e., the angle of emergence e is equal
40° e igit to the angle of incidence i. Thus, the emergent ray
BC is parallel to the incident ray A0.
3 60°
4 70°
5. S0
Average = INCDET
AJR
GLASS
BLOCK
RAY
From the above observation table, we find that
M
sin i DF
the raio comes out to be a constant REFRACTED
sin r EG RAY

for each value of angle i. This verifies the second

DIRECT ON OF
AIR

lax of refraction. The ratio so obtained is equal

to the refractive index u of glass, the material of
the block. Thus, the refractive index u of glass
M,
EMRGNT N
Fig. 4.7 Refraction through a rectangular glass block
RAY
or of any other material in the form of a block
can be determined. Lateral displacement
Further, the incident ray A0, the normal NOM In Fig. 4.7, we observe that due to refraction
at the point of incidence O and the refracted ray of light at two parallel surfaces of a parallel sided
OB are in the plane of paper (ie, in the same glass block, the angle of emergence is equal to the
plane). This verifies the first law of refraction.angle of incidence, so the emergent ray BC and the
4.6 REFRACTION OF LIGHT THROUGH A incident ray AO are parallel (i.e., they are in the
RECTANGULAR GLASS BLOCK same direction), but they are not along the same
line. The emergent ray is laterally displaced from
Fig 4.7 shows a rectangular glass block the path of the incident ray The path of the
PQRS. A light ray AO falls on the surface PQ. incident ray AO in absence of glass block has been
NOM is the normal to the surface PQ at the point shown in Fig. 4.7 by the dotted line OD. The
of incidence O. At he surface PQ, the ray A0 perpendicular distance XY (= x), berween the path
enters from air (rarer medium) to glass (denser of emergent ray BC and the
Inedium), so it slows down and bends towards the ray OD is called lateral direction of incident
displacement.
81
The lateral displacement xdepends on*
0Y The thickness of the block (or medium) :
More the thickness of the medium, more
is the lateral displacement. A
M
(Y The angle of incidence : More the angle
of incidence, more is the lateral
displacement.
The refractive index of the medium and
the wavelength of light used : More
MEO the refractive index of the medium,
more is the lateral displacement. Since
refractive index increases with the Fig. 4.8 Multiple reflections in a thick mirror
decrease in wavelength of light, so lateral
displacement increases with the decrease 4%) is reflected in the direction BP, fotina
in wavelength of light (i.e., lateral faint virtual image at A,, while a larger fras
displacement is more for violet light than of light (nearly 96%) is refracted along
for red light). inside the glass. The ray BB' which strikes a
4.7 MULTIPLE IMAGES INA THICK PLANE surface PN inside the glass as B'C. This ray
is now strongly reflected back by the silve
GLASS PLATE OR THICK MIRROR then partially refracted along CQ in aír a
fa pin (or an illuminated object) is placed partially reflected along CC within the glass. 1
in front of a thick plane glass plate (or a thick refracted ray CQ forms the virtual image A,.
mirror) and is viewed obliquely, anumber of image A, is the brightest image because
images are seen. Out of these images, the second 1ormed due to the light suffering a strong f
image is the brightest, while others are of reflection at the silvered surface PN.
decreasing brightness. The reflected ray CC further suffers multi
In Fig. 4.8, LMNP represents a thick plane reflections at C, D, D, and refractions at
mirror of which NP is the silvered surface. An E, F, within the thickness of the glass pl
illuminated object A is kept in front of it. giving rise to multiple virtual images A,, A,, A
Consider two rays, one falling normally on the of gradually decreasing brightness.
mirror and the other AB falling obliquely on it.
When the ray of light AB falls on the surface LM Note : () In Fig. 4.8 due to drawing, th
of the mirror, a small fraction of light (nearly rays BP, CQ, .. appear to be far
separated
from each other, but actually they enter the eye
Laleral displacement x= 1sin (i-r) where t = thickness of glass simultaneously.
COS r
block, i= angle of incidence, r = angle of refraction, In case of (2YA thick glass plate also bchaves like a
white light, for a given angle i, the angle ris different for different thick plane mirror.
colours, so the lateral displacement is also different.

82
 (B) REFRACTION OF LIGHT THROUGH A PRISM

4.8 PRISM 4.9 REFRACTION OF LIGHT THROUGH A

GLASS PRISM
Aprism is a transparent medium bounded
Fig. 4.23 shows the principal section ABC of
by five plane surfaces with a triangular cross
section. a glass prism. The angle of prism is BAC = A.
Let us consider a monochromatic ray of light (i.e.,
Tvo opposite parallel surfaces of a prism are a light ray of single colour) OP striking the face
identical triangles, whle the other three surfaces AB of the prism at an angle of incidence i,. It
are rectangular and inclined to each other. suffers refraction from air (rarer medium) to glass
Fig, 4.22 shows a prism in which the opposite (denser medium) at the face AB, so the ray bends
narallel surfaces ABC and DEF are triangular. The towards the normal PN making an angle of
principal of the prism is the triangle ABC. refraction r, and travels along PQ inside the prism.
BAC is the angle of prism, which is denoted by Thus, PQ is the refracted ray. The refracted ray PQ
the Jeter A. The two rectangular surfaces ABED now strikes the face AC of the prism at an angle of
and ACFD shown shaded are polished which act incidence r,. It suffers refraction from glass (denser
as the refracting surfaces. The line AD is the medium) to air (rarer medium) at the face AC, so the
refracting edge and the rectangular surface BCFE ray bends away from the normal NQ and emerges
is the base of the prism, which is usually out of the prism as QR at an angle of emergence i,.
grounded or made rough. Thus, QR is the emergent ray.
REFRACTING EDGE. A

A
ANGLE
OF
DEVIATION
REFRACTING
SURFACE
M
REFRACTING 8
SURFACE

EM RAYRGENT
INCIDEN
RTAY

BASE

Fig. 4.22 Prism B

R
Fig. 4.23 Deviation by aprism
Note : (1) The two refracting surfaces of a
prism are not parallel to each other, but they are Note : Due to the principle of reversibility
Inclined on each other making an angle A called of path of a light ray, if a ray directed along RQ
the angle of prism. is considered as the incident ray, it will follow
2) In ray diagrams, a prism is usually shown the path QPO. It means that for the incident ray
only by its principal section ABC. RQ, the emergent ray will be PO.
89
 Thus in pasing through a prism, a ray of light Hence from cqns. (4.9) and (4.10),
suffers refraction at two inclincd faces AB and AC 8= i, + i) -A
of the prism. In each refraction, the ray bends or i, + i, = A+ 8
towards the base of the prism, At the fist face AB
of the prisn the ray OP, instead of going along Note : In a prism, the refraction of Jioh:
..4.11)*
OPM. has bent at P along PQ. so it suffers a Occurs at two inclined faces, so the
deviation by an MPQ qual to ,. At the second ray is not parallel to the incident ray, but it i
face AC, the ray PQ has bent at Q along QR which deviated towards the base of the
emergent
prism. On the
appears to be coming along MQR, So it suffers a other hand, in a parallel sided glass slab, the
deviation by an MQP equal to d,: refraction of light occurs at two parallel faces.
In the atsence of the prism, the incident ray so the emergent ray is parallel to the incident
OP would have travelled along OPML but the ray with a lateral displacement.
prism has deviated it along QR. The emergent ray
QR appears to be coming along MQR. Thus, the Factors affecting the angle of deviation
prism has produced a total deviation in the incident The angle of deviation (i.e., the deviation
ray by an LMQ. which is the angle between the produced by a prism) depends on the folowin
direction of incident ray (OP produced forward) four factors
and the emergent ray (QR produced backward). It ( the angle of incidence (i),
is called the angle of deviation and is denoted by
the grek alphabet (delta).
(Y the material of prism (i.e., on efractive
index ),
In Fig. 4.23, Z LMQ= MPQ+ Z MQP 3Y the angle of prism (A ), and
Angle of deviation = , + &, (4 the colour or wavelength (2) of light used.
Since Z MPN = i, (angle of incidence), and
(1) Dependence of angle of deviation on angle
ZMQN =L (angle of emergence),* of incidence; i-8 graph
Therefore ZMPQ = 8, =i-) It is experimentally observed that as the angle
and ZMQP = 8, =(, of incidence increases, the angle of deviation first
: From eqn. (). 8 = (i, -r) +(i, -) decreases, reaches to a minimum value for a
or ..(4.9) certain angle of incidence and then on further
increasing the angle of incidence, the angle of
Also for the quadrilateral APNQ in Fig 4.23, deviation begins to increase.
LAPN = LAQN = 90°
Note : To get the graph showing the variation
.: Z PNQ+Z PAQ = 180° of angle of deviation with the angle of incidence
But Z PAQ = A, experimentally, the direction of incident ray is
ZPNQ = 180° -A ...ii) kept unchanged and the prism is rotated. On
rotation of the prism, the direction of nomal at
But in triangle PNQ.
..i)
the face of the prism changes, so the angle which
ZPNQ = 180°- (r,+ r) the incident ray makes with the normal (i.e.,
From eqns. (ii) and (ii), angle of incidence) changes. The angle of
[180° - (r t r,) = 180° - A deviation ô is noted for each angle of incidence
or ...4.10) iand then a graph is drawn for d vs i.

Sometimes angle of emergence is denoted by the letter e in * If angle of incidence is i and angle of emergence is e, then
eqn. (4.11) takes the form i +e=A+ .
place of i, then angle of incidence is written i in place of i,
90
 Fig.
4.24 shows the variation of angle of incidence i, = 70, angie of emergence I = 33
with angle of incidence (i). It is and angle of deviation 8 = 43°. In Fig. 4.25(b),
deviation(8) in which the minimum value i, =
i-òcurve 48, i, = 48° and × = 36°, while in
calledthe deviation is marked as ..ee
of Fig. 4.25c), i, = 30, i, = 77° and =47°. These
ofangle angles are calculated using the following relations:
(8) sin i,
DEVIATION For refraction at the first face. u= r, is
sin r,
obtained.

OF
Now I+,= A, so r, (the angle of incidence
at second surface) is calculated.
ANGLE SIn r
For refraction at the second face.
sin i
ANGLE OF INCIDENCE () ’
so i, (angle of emergence) is obtained.
Fig. 4.24 i-S curve
Thus, &=(i, + i,) -Ais calculated.
Tt is observed that the angle of deviation is is A
incidence
minimun (= min) When the angle of
i.e., when
equaltothe angle of emergence ABC is
43
4.23, if A
or when r;= In Fig.
R
70
equilateral (or equiangular), for =,, the ray PQ s8.5
BC.
willbe parallel to the base (a) When 70"
The position of a prism with respect to the
incident ray at which the incident ray suffers
minimum deviation is called the position of P
48° 48 30°/
170

minimum deviation. Thus, in the position of 30 30° 19.5 77

minimum deviation, the refracted ray inside the ó B

prism is parallel o its base if the prism is (b) When i, = 48° B (C) When a30°
equilateral (or the principal section of the prism Fig. 4.25 Deviation by a equilateral prism
forms an isosceles triangle). In other words, at different angles of incidence
In the position of minimum deviation, From the ray diagrams shown in Fig. 4.25, it
can easily be inferred that &has the minimum
ie, when 8= Ômins i =i,=i (say). value in Fig. 4.25(b) when the angle of incidence
Then from eqn. (4.11), i, is 48° and the refracted ray PQ is parallel to the
Omin = 2i -A .(4.12) base BC of prism. In this condition, the angle of
(equal to the angle of
For a given prism and given colour of light. emergence ly S also 48°
incidence i, ). In Fig. 4.25(b) the angle of
Omin 0S unique since only one horizontal line can be minimun deviation is
drawn parallel to i-axis at the lowest point of i-ð
Curve, i.e., only for one value of angle of o=2i-A=2x48°-60
min
=36°.
Incidence i, the refracted ray inside the prism is (2) Dependence of angle of deviation on the
parallel to its base. Al other values of (e.g. o,) material ofprism (or refractive index)
are obtained for two other values of angle of It is found that for a given angle of incidence,
incidence i, and i, as shown by the dotted curve. a prism with a higher refractive index produces
Deviation at different angles of incidence : greater deviation than a prism which has a lower
ig 425 shows the deviation of a light ray by an refractive index Aflint glass prism produces more
Cyulateral prism of glass (u = 1-5) at different deviation than a crown glass prism of same
angles of incidence. In Fig. 4.25(a), angle of refracting angle smce piu erown'
91
(3) Dependence of angle of deviation on the medium is different for the light of
angle of prism* colours. It decreases with the
It is found that the angle of deviation (8) wavelength of light. Thus, for visible
increase dif ers
increases with the increase in the angle of refractive index of the nmaterial of a
prism (A). maximum for violet colour and prisa
(4) Dependence of angle of deviation on the red colour. Consequently, a given pr minimum
deviates violet light the most and red light the t
colour (or wavelength) of light
red).
The refractive index of a given transparent (.e.,oyiolet >Ored Since yiolet
For smallangle of prismn A, angle of deviation = (u-1)A.
orgent
EXAMPLES
 (C) SIMPLE APPLICATIONS OF REFRACTION OF LIGHT

4.10 REAL AND APPARENT DEPTHosC E ray of light OA, starting from the object O, is
incident on the surface PQ normally, so it passes
An object placed in a denser medium when undeviated along the path AA'. Another ray OB,
viewed from ararer medium, appears to be at starting from the object O, strikes the boundary
depth lesser than its real depth. This is surface PQ at B and suffers refraction. Since the
because of refraction of light. ray travels from a denser medium (water or glass)
In Fig. 4.36, consider a point object O kept at to a rarer medium (air),the
drawn at
so it bends away from the
point of incidence B on
ne bottom of a transparent medium (such as water normal NBN
and travels along BC in air.,
Or glass) separated from air by the surface PO. A the surface PQ
95
 A
:. Refractive index of medium
with
mba
OB
IB
respeA
Since point Bis very close too
P
A B AIR
the object is viewed from a point A, i.e, point
REAL
DEPTH
APPARENT
DEPTH
I WATER OR GUASS
I(DENSER MEDIUM) the object 0, .:. IB = IA and OB = OA. a vertically
real depth
Hence, m IA apparent depth
Fig. 4.36 Real and apparent depth . 4.1,
real depth
Apparent depth =
Note : The point B is very close to the point aPm .4.14
A, and both the rays OA and BC enter the
eye Examples
simultaneously. Fig. 4.36, they have been
In
(i) For glass, 3
shown separately for the sake of clarity of the = 2: therefore the
ray diagram. the glass slab appears only two-thirdthiof ckness dj
its Te
When viewed by the eye, the ray BC thickness when it is viewed from air b
to be coming from a point Iwhich is the appears keeping the eye vertically above the slab.
virtual 4
image of 0, obtained on producing A'A and CB (ii) For water, 3 therefore the depth of
backwards. Thus any object (e.g. a coin) placed at water pond appears three-fourth of its real degt
0, when seen from above (air), will on seeing it from air in a nearly vertical
appear to be
at I which is at a lesser depth (= Al) than direcia
its actual (i.e., it appears shallow). This is why a fish wha
depth (= AO). seen from air appears to be nearer to the surfac
In Fig. 4.36, for the incident ray of water than at its actual depth.
OB, angle of
incidence i= Z0BN' and angle of refraction urther,
r= ZCBN. Since AO and BN are
parallel and OB Shift OI = real depth- apparent
is a transversal line, so depth
ZAOB = Z0BN' =i
Similarly, IA' and BN are parallel and IC is the Shift = real depth X .(4.15
transversal line, so
ZBIA = ZCBN =r The shift by which the object
Now in right-angled triangle BAO, raised, depends on : appears to bë
(1) the refractive index of the
sin i = BA
(2) the thickness of the denser
medium,
OB medium, and
and in right-angled triangle IAB, (3) the colour (or wavelength) of incident lighi
ag (1) Dependence of shift on the
sin r= BA refracthh
IB index : Higher the refractive index of the
For refraction from medium (water or medium, more is the shift.
to air, by Snell's law glass)
(2) Dependence of shift on the thickness of th
sin i
sin r
medium :For a given medium, shift is dire
sin i
proportional to the thickness of mediu
or BA/OB IB Thicker the medium, more is the shitt.
sin r BA/IB OB The refractive index ofa medium increases withthe decreast
in wavelength of incident light (Hy > R
96
 Dependence on wavelength (or colour) of
(3)light: The shift decreases with the increase Note : An object placed in a rarer medium
wavelength of the light used. Since when viewed from a denser medium appears to
in the
therefore the shift is more for violet be at a greater distance than its real distace.
In Fig. 4.38, an object O placed in air when
licht than for red light in a given medium. viewed from inside a water body appears lo be
Note : The apparent depth of an object lying at I which is higher than the object 0.
medium is always less than its real
in a denser
denth when viewed from any direction in the
rarer medium. But the
above cqns. (4.13), (4.14)
and (4.15) are valid only when the object is
seenfrom vertically above. AIR A RARER
B
A11 APPARENT BENDING OF A STICK WATER DENSER

UNDER WATER
Fig. 4.37 shows a straight stick (or pencil)
XOP placed obliquely in water. The portion OP of
the stick (or pencil) under water when seen from Fig. 4.38 An object in rarer medium
viewed from a denser medium
air appears to be shortened and raised up as OP.
This is due to refraction of light from water to 4.12 SOME CONSEQUENCES OF REFRACTION
OF LIGHT
air. The rays of light coming from tip P of the
stick (or pencil), when cross the water - air In our daily life we come across many
interface, bend away from the normal at the phenomena which are caused by refraction of
of these are given below :
interface and appear to be coming from a point light.(1) Some
A star appears twinkling in the sky due to
P which is the virtual image of the point P. The
same is true for every point of the stick (or fluctuation in refractive index of air with
pencil) inside water fromn P to O. temperature.
EYE
(i) The sun is seen a few minutes before it rises
above the horizon in the morning while in
X STICK the evening few mninutes longer after it sets.
AIR (iii) Acoin kept in a vessel and not visible when
WATER seen from just below the edge of the vessel,
can be viewed from the same position when
P
water is poured into the vessel.
(iv) The print on paper appears to be raised
Fig. 4.37 Bending of stick due to refraction when a glass slab is placed over it.
A pece of paper stuck at the bottom of a
Ihus, the part PO of the stick (or pencil)()
appears to be P'O, i.e., the immersed part of the glass slab appears to be raised when seen
from above.
stick appears to be raised and therefore bent at
the point Oat the surface of water and the stick (vi) A water tank appears shallow than its actual
(or pencil) XOP appears as XOP . depth.
(viü) A person's legs as seen from outside appear to
be short when standing in a pool or water tank.

97