PHYSICS SELF NOTES
Light Part 1 – Refraction Of Light @ Plane Surfaces
(A) Refraction, Laws of Refraction & Refractive Index
The return of light in the same medium after striking a polished surface
is called reflection of light.
Reflection of a light ray obeys two laws:
(i) the angle of reflection is equal to the angle of incidence
(ii) the incident ray, the normal at the point of incidence and the
reflected ray, all lie in one plane.
Light travels at a constant speed in a transparent
homogeneous medium.
REFRACTION OF LIGHT
Partial reflection and refraction at the boundary of two
different media: In a transparent homogeneous medium light travels
with a constant speed in a straight line path, but when a ray of light
travelling in one transparent medium strikes obliquely at the surface of
another transparent medium, a part of light goes back to the same
medium obeying the laws of reflection and is called the reflected light.
The remaining part of light enters into the other medium and travels in
a straight path but in a direction different from its initial direction and
is called the refracted light.
Thus, at the boundary separating Optical density has no relation
the two media, light suffers partial with the density of medium.
reflection and partial refraction. Kerosene is less dense than water
(as it floats on water), but it is
The change in the direction of the
optically denser than water.
path of light, when it passes from
one transparent medium to The optical density of a medium
another transparent medium, is depends on the speed of light in
called refraction. The refraction of that medium, while the density of
light is essentially a surface a medium depends on its inter-
phenomenon. molecular separation.
It has been experimentally observed that:
medium (say, from air to glass), it bends towards the normal (i.e., ∠r <
(1) When a ray of light travels from a rarer medium to a denser
∠i). Deviation = i - r
(2) When a ray of light travels from a denser medium to a rarer
∠r > ∠i). Deviation = r - i
medium (say, from glass to air), it bends away from the normal ( i .e.,
(3) The ray of light incident normally on the surface separating the two
media, passes undeviated (i.e., such a ray suffers no bending at the
surface). Thus, in case of light incident normally i.e. when angle of
incidence angle i = 0°, then angle of refraction angle r = 0°.
The deviation of the ray is zero (i.e., Deviation = 0°)
Cause Of Refraction (Or Cause Of Change In Direction)
When a ray of light passes from one medium to another medium, its
direction (or path) changes because of the change in speed of light in
going from one medium to another.
In passing from one medium to another, if light slows down, it bends
towards the normal and if light speeds up, it bends away from the
normal. If the speed of light remains the same in passing from one
medium to another, the ray of light does not bend. It passes
undeviated.
Note: In case of normal incidence (angle i = 0°) for light passing from
one medium to another, the speed of light changes but the direction of
light does not change.
LAWS OF REFRACTION
Refraction of light obeys two laws of refraction which were given by the
Dutch scientist Willebrod Snell, so they are known as Snell's laws after
his name. They are:
(1) The incident ray, the refracted ray and the normal at the point of
incidence, all lie in the same plane.
(2) The ratio of the sine of the angle of incidence i to the sine of the
angle of refraction r is constant for the pair of given media.
i.e., mathematically
The constant ₁μ₂ is called the refractive index of the second medium
with respect to the first medium. Here the Greek letter μ (mew) is the
symbol used for refractive index.
REFRACTIVE INDEX
The refractive index of the second medium with respect to the first
medium is defined as the ratio of the sine of the angle of incidence in
the first medium to the sine of the angle of refraction in
the second medium.
Unit: The refractive index has no unit as it is the ratio of two similar
quantities.
EFFECT ON SPEED (V), FREQUENCY (F) AND WAVELENGTH (Λ)
DUE TO REFRACTION OF LIGHT
1. When a ray of light gets refracted from a rarer to a denser medium,
the speed of light decreases; while if it is refracted from a denser to a
rarer medium, the speed of light increases.
2. The frequency f of light does not change on refraction as it depends
on the source of light.
3. The wavelength changes on refraction. The speed of light V in a
medium is related to the frequency f and its wavelength (in that
medium), as: V = f × λ
When light passes from a rarer to a denser medium, the wavelength
decreases (since speed of light decreases, but its frequency remains
unchanged).
When light passes from a denser medium to a rarer medium, its
wavelength increases as the speed of light increases.
SPEED OF LIGHT IN DIFFERENT MEDIA
The refractive index of a medium is defined as the ratio of the speed of
light in vacuum (or air) to the speed of light in that medium, i.e.,
The refractive index of a transparent medium is always greater than 1
(it cannot be less than 1), because the speed of light in any medium is
always less than that in vacuum (i.e., V < c ). Obviously μ = 1 for air or
vacuum.
On general μ of 2nd medium with respect to 1st medium is related to
the speed of light in the two media as:
Note: If the refractive indices of medium 1 and medium 2 are
the same, the speed of light will be the same in both the
media, so a ray of light will pass from medium 1 to medium 2
without any change in its path even when the angle of
incidence in medium 1 is not zero.
CONDITIONS FOR A LIGHT RAY TO PASS UNDEVIATED ON
REFRACTION
A ray of light passes undeviated from medium 1 to medium 2 in either
of the following two conditions :
(i.e., ∠i = 0° so ∠r = 0°)
(1) When the angle of incidence at the boundary of two media is zero
(2) When the refractive index of medium 2 is the same as that of
medium 1 (i.e., ¹μ = μ², i = r)
FACTORS AFFECTING REFRACTIVE INDEX OF A MEDIUM
LATERAL DISPLACEMENT
The distance or gap (perpendicular distance) between the
path of the emergent ray and incident ray is known as lateral
displacement or d.
LATERAL DISPLACEMENT OF A MEDIUM DEPENDS UPON
If a pin (or an illuminated object) is placed in front of a thick plane
glass plate (or a thick mirror) and is viewed obliquely, a number of
images are seen. Out of these images, the second image is the
brightest, while others are of decreasing brightness.
(B) Refraction Of Light Through A Prism
PRISM
A prism is a transparent medium bounded by five plane surfaces with a
triangular cross section.
Two opposite parallel surfaces of a prism are identical triangles, while
the other three surfaces are rectangular and inclined to each other.
The two refracting surfaces of a prism are not parallel to each other,
but they are inclined on each other making an angle A called the
angle of the prism.
In a prism, the refraction of light occurs at two inclined faces, so the
emergent ray is not parallel to the incident ray, but it is deviated
towards the base of the prism. On the other hand, in a parallel sided
glass slab, the refraction of light occurs at two parallel faces, so the
emergent ray is parallel to the incident ray with a lateral displacement.
FACTORS AFFECTING THE ANGLE OF DEVIATION
(C) Simple Applications Of Refraction Of Light
REAL AND APPARENT DEPTH
An object placed in a denser medium when viewed from a rarer
medium, appears to be at a depth lesser than its real depth. This is
because of refraction of light.
SHIFT OF WHICH THE OBJECT APPEARS TO BE RAISED
DEPENDS UPON
SOME CONSEQUENCES OF REFRACTION OF LIGHT
In our daily life we come across many phenomena which are caused by
refraction of light. Some of these are given below:
(i) A star appears twinkling in the sky due to fluctuation in refractive
index of air with temperature.
(ii) The sun is seen a few minutes before it rises above the horizon in
the morning while in the evening few minutes longer after it sets.
(iii) A coin kept in a vessel and not visible when seen from just below
the edge of the vessel, can be viewed from the same position when
water is poured into the vessel.
(iv) The print on paper appears to be raised when a glass slab is placed
over it.
(v) A piece of paper stuck at the bottom of a glass slab appears to be
raised when seen from above.
(vi) A water tank appears shallow than its actual depth.
(vii) A person's legs as seen from outside appear to be short when
standing in a pool or water tank.
(C) Critical Angle & Total Internal Reflection
TRANSMISSION OF LIGHT FROM A DENSER MEDIUM (GLASS
OR WATER) TO A RARER MEDIUM (AIR) AT DIFFERENT
ANGLES OF INCIDENCE
CASE (I) when the angle of incidence is small (i < C): If the
angle of incidence i is gradually increased, the angle of refraction
also increases, but the intensity of refracted ray keeps on
decreasing. Finally, the angle of refraction r reaches its maximum
possible value equal to 90° at a certain angle of incidence i = C.
Here C is called the critical angle.
CASE (II) when the angle of incidence is equal to the
critical angle (i = C):
CASE (III) when the angle of incidence is greater than the
critical angle (i > C):
CRITICAL ANGLE
Critical angle is the angle of incidence in the denser medium
corresponding to which the angle of refraction in the
rarer medium is 90°.
FACTORS AFFECTING CRITICAL ANGLE
TOTAL INTERNAL REFLECTION
When a ray of light travelling in a denser medium, is incident at
the surface of a rarer medium at an angle of incidence greater
than the critical angle for the pair of media, the ray is totally
reflected back into the denser medium. This phenomenon is called
total internal reflection.
ESSENTIAL CONDITIONS FOR TOTAL INTERNAL REFLECTION
There are two necessary conditions for total internal
reflection:
(1) The light must travel from a denser to a rarer medium.
(2) The angle of incidence must be greater than the critical angle
for the pair of media.
Note: In the process of total internal reflection, 100%
energy (or intensity) of light is reflected back. No other
device such as plane mirror, etc. produces 100% reflection
(due to absorption and refraction of some part of light).
Due to this property, the phenomenon of total internal
reflection is used in the construction of periscope,
binocular and certain types of cameras in which a total
reflecting prism replaces a plane mirror for
reflection of light.
USE OF A TOTAL INTERNAL REFLECTING PRISM IN PLACE OF
A PLANE MIRROR
A total internal reflecting prism is some light is refracted and
used in place of a plane mirror to absorbed, so the reflection is not
deviate a light ray by 90° in a 100%.
periscope and by 180° in a
Thus the image obtained by the
binocular as well as in a camera.
use of a total reflecting prism, is
The reason is that due to total much brighter than that obtained
internal reflection in the prism, by using a plane mirror. Further
the entire incident light (100%) is the brightness of image formed
reflected back into the denser by a total reflecting prism always
medium, whereas in ordinary remains unchanged, while in a
reflection from a plane mirror, plane mirror due to deterioration
of silvering after a long use, the image formed by
it becomes faint.
SOME CONSEQUENCES OF TOTAL INTERNAL REFLECTION
In our daily life, we observe many consequences of total internal
reflection. Some of these are given below:
(1) On a hot sunny day, a driver may see a pool of water (or wet
road) in front of him at some distance. It is the phenomenon of
mirage which is often observed in a desert.
(2) An empty test tube placed in water in a beaker with its mouth
outside the water surface, shines like a mirror when seen at
certain angles.
(3) A crack in a glass vessel often shines like a mirror.
(4) A piece of diamond sparkles when viewed from certain
directions.
(5) An optical fibre is used to transmit a light signal over a long
distance without any loss of energy.
