ARMY PUBLIC SCHOOL

GORAKHPUR

PHYSICS INVESTIGATORY PROJECT

SESSION 2024-2025

SUBMITTED BY: SUBMITTED TO:

SAURABH SAHANI DEPARTMENT OF PHYSICS
  CERTIFICATE

This is to certify that SAURABH SAHANI , a

student of class XII – A , has successfully
completed the investigatory project on
Dependence of angle of deviation on angle of
incidence using hollow prism filled with
different transparent fluids under the guidance
of Mr. SIKANDAR KUSHWAHA (PGT PHYSICS)
during the year 2024-2025 .

Teacher’s signature Examiner’s signature

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 ACKNOWLEDGMENT

In the accomplishment of this project successfully,

many people have best owned upon me their
blessings and the heart pledged support, this time
I am utilizing to thank all the people who have
been concerned with project.
I would like to thank my classmates who have
helped me a lot & also, Lab Attendant:
Nagendra Rawat.
Primarily I would thank God being able to
complete this project with success. Then I would
like to thank my principal and my Physics teacher:
Sikandar Kushwaha whose valuable guidance has
been the ones that helped me patch this project
and make it full proof success. His suggestions
and his instructions have served as the major
contributor towards the completion of the
project.

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 INDEX

Cover page
Certificate
ACKNOWLEDGMENT
Index
Aim
Apparatus and Material Required
Theory
PROCEDURE
OBSERVATIONS
Graphs
CALCULATIONS
Result
PRECAUTIONS

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  Aim:
TO INVESTIGATE THE DEPENDENCE OF THE
ANGLE OF DEVIATION ON THE ANGLE OF
INCIDENCE USING A HOLLOW PRISM
FILLED, ONE BY ONE, WITH DEFFERENT
TRANSPARENT FLUIDS.

 Apparatus and Material Required:

 Drawing board
 Hollow prism
 Pins
 White paper sheets
 Protractor
 Ruler
 Pencil
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 Theory
Refraction through a prism :
Deviation produced by a prism.
Figure→ shows the path PORS
of a ray of light suffering
refraction through a triangular
glass prism. The angle between
the directions of the incident ray
PQ and the emergent ray RS is
called the angle of deviation, &
Let i and r be the angles of incidence and refraction at the face AB,
and r' and e be angles of incidence and emergence at the face AC.
Let A be the angle of the prism.
From the quadrilateral AQNR, A+ ∠QNR =180°
From ΔQNR, r+r’+∠QNR=180° ∴A=r+r’
δ= ∠MQR+ ∠MRQ=(i-r)+(e-r’)=i+e-A
or i+e=A+ δ or Angle of incidence + Angle of emergence =
Angle of prism + Angle of deviation
So, when a ray of light is refracted through a prism, the sum of the
angle of incidence and the angle of emergence is equal to the sum of
the angle of the prism and the angle of deviation.

Variation of angle of deviation with angle of

incidence, Figure→ shows the variation of
angle of deviation δ with the angle of incidence
i. For a given prism and for a green colour of
light, the angle δ depends on i only.

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As i increases, the angle δ first decreases and reaches a minimum
value δm and then increases. Clearly, any given value of δ
corresponds to two angles of incidence i and e.
The minimum value of the angle of deviation suffered by a ray on
passing through a prismn is called the angle of minimum deviation
and is denoted by δm or Dm.

Relation between refractive index and angle of minimum deviation.

When a prism is in the position of minimum deviation, a ray of light
passes symmetrically (parallel to the base) through the prism so that
i=e, r=r', δ=δm
As A+ δ=i+e
∴ A+ δm =i+i or i=
Also A=r+r'=r+r=2r ∴ r=
From Snell's law, the refractive index of the material of the prism will
be

μ= =

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 PROCEDURE
1. Fix a sheet of white paper on the drawing board with drawing
pins/cellotape. Draw a long straight line XY in the middle of the
paper and parallel to its longer side. Mark six points O 1,O2,… , O6
at suitable (a few cm more than the side of the prism) and equal
distances on the line. Draw perpendiculars O1 N1, O2 N2, ... , O6N6
on this line
2. Draw incident rays at the points O1, O2, ... , O6 making angles of
incidence of 35°, 40°, 45°, 50°, 55° and 60° respectively with the
normals, using a protractor.
3. Fill the hollow prism with water and close its plastic lid. Dry drops
of water, if any, sticking on its outer surface.
4. Place the prism with its refracting face AB on the line XY with
point O1 in the middle of AB. Draw the boundary of the prism
with a sharp pencil.
5. Fix two pins P1 and Q1 on the incident ray already marked.
Looking into the prism from the opposite refracting face AC,
position the eye in such a way that the feet of P1 and Q1 appear
to be one behind the other. Now fix pins R1 and S1 in line with P1
and Q1 so as viewed through the prism.
Keep the eye at some distance from the
pins so that all the pins can be seen in
clear focus simultaneously, as shown in
Fig → Distances P1Q1 and R1S1 should
not be less than 6 cm so as to locate the
directions of the incident and emergent
rays accurately.

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6. Remove the pins and encircle their pin pricks. Draw the line
joining R1 and S1. Produce lines P1Q1 and R1S1 so that they meet
at point M1. Measure the angle of incidence i= ∠P101 N1 and the
angle of deviation δ = ∠ S1MT.
7. Repeat the experiment with angles of incidence like 40°,45°,50°,
55° and 60° and measure the corresponding angles of deviation
in each case.
8. Repeat the experiment by filling the hollow prism with air and oil.
Note the values of i and δ.
9. Note the angle of the prism.

 OBSERVATIONS
Least count of the protractor= _________degrees

Angle of prism, A= _______ degrees

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  Variation of angle of deviation 8 with angle of incidence i for a
hollow prism filled with different transparent fluids

Angle of Angle of deviation 8 for hollow prism filed with

S.N0. incidence i
(degrees) Water Ethyl alcohol oil
1.
2.
3.
4.
5.

 PLOTTING THE GRAPHS BETWEEN i AND δ

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 i vs δ graphs

 CALCULATIONS
Draw tangent on the lowest point of each graph parallel to the
X-axis and note the value of angle of minimum deviation δm, on
the Y-axis for each liquid.
(i). Angle of minimum deviation for water,
δm= ______degrees
Refractive index of water, μwater = ______
(ii). Angle of minimum deviation for ethyl alcohol,
δm= ______degrees
Refractive index of water, μalcohol = ______
(iii). Angle of minimum deviation for kerosene oil,
δm= ______degrees
Refractive index of water, μoil = ______

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 RESULT
1. As the angle of incidence increases, the angle of
deviation first decreases, reaches a minimum
value and then again increases, as is obvious
from the U-shaped i versus δ graph.
2. Angles of minimum deviations are
δm (water)= ______degrees,
δm (alcohol)= ______degrees,
δm (oil)= ______degrees
3. Refractive indices of the transparent fluids are
μwater = ______,
μalcohol = ______,
μoil = ______

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 PRECAUTIONS
1. Same angle of prism should be used for all observations
2. The angle of incidence should not be less than 30°, as the ray
may get totally reflected inside the prim.
3. For prisms of side 2.5 or 3 cm, the distance between any two
pins should not be less than 6 cm.
4. Pins should be fixed vertically and the pin pricks should be
encircled immediately after they are removed.
5. The feet of the pins (and not their heads) should be in the same
straight line.
6. Indicate the path of the incident, the refracted and the
emergent rays by arrowheads.
7. A smooth best fitting curve should be drawn through the
plotted points.
8. Position of the prism should not be disturbed for a given set of
observations.
9. After filling the hollow prism with a liquid, it should be covered
properly by its plastic lid. Also, liquid drops left on its outer
surface should be dried with a tissue paper.

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