Submitted By: Madhav Tandon Class
: XII-A1
Roll No.: 18
This is to certify that Madhav Tandon, a student of class XII has successfully completed the investigatory project on the topic, “To find out the refractive index of various liquids using a Hollow Prism.” under my guidance. This Project is absolutely genuine and does not indulge in plagiarism of any kind. The references have been declayered at the end of this report.
Signature Mr. Anurag Chitra
Signature Principal
CONTENTS Sl. No 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Item Objective Introduction Apparatus Theory Procedure Observations Diagrams Calculations + Graphs Precautions Bibliography
Page No.
OBJECTIVES:
To study the variation of the angle of deviation with the angle of incidence using Hollow Glass Prism and to determine the angle of minimum deviation.
To find out the refractive index of various liquids using a Hollow Prism. INTRODUCTION:
T his project is of Investigatory Type. In this project, a hollow prism has been used to calculate the refractive index of various liquids. The hollow prism is filled with liquid and then the experiment is performed.
APPARATUS:
Drawing Board
Sheet of Paper
Hollow Glass Prism
Graph Paper
Protractor
Drawing Pins
All Pins
Pencil
THEORY:
Refractio n :
In a homogenous medium, light travels along a straight line,but whenever it falls on a surface of another medium, a very small fraction of it is reflected back and most of the light passes into the medium, though with a change of direction. This phenomenon of the bending of light at the surface of separation of the two medium is called refraction of light. C au s e s o f r e f r ac t i o n :
This phenomenon of refraction takes place when a beam of light enters a medium in which light enters a medium in which light travels with a different velocity. L a w s O f R ef r ac t i o n :
1. The incident ray, the refracted and the normal to the surface at the point of incidence lie on the same plane. 2. For any two given media, the ratio of the sine of the angle of incidence to the angle of refraction is a constant, where it is the angle of incidence and is the angle of refraction.
M e d i u m : The surrounding substance through which the light travels. For a monochromatic light, the ratio of the sine of the angle of incidence to the sine of angle of refraction is a constant for any two given media. If `I’ is the angle of incidence, and `r’ is the angle of refraction, then; Sine( I) ------Sine( R)
=
Constant
the constant is called the refractive index. For most purposes it may be assumed that the refractive index is with respect to air. When light travels from a rarer to a denser medium, it bends towards the normal and vice versa when it goes from a denser to a rarer medium. It has been experimentally shown that Refractive index of substance =
Velocity of light in air -----------------------------------Velocity of light in substance
R ef r ac t i o n T h r o u g h P r i s m : A transparent medium bounded by two plane surface inclined to each other at an angle is called a Prism. The angle between the two faces is known as the angle of the prism. : The angle through which the incident [C1] A n g l e o f d e v i at i o n ray of light is deviated is called the angle of deviation. In fact it is the angle between the emergent ray and the incident ray produced.
A n g l e o f m i n i m u m d e v i at i o n : As the value of the angle of incidence (1) increases, the angle of deviation decreases till for a particular value of the angle of incidence, it attains a minimum value m , is called the angle of minimum deviation. Critical angl e :
It is that angle of incidence in the denser medium for which corresponding angle of refraction in the rarer medium is 90 degree. I = --------Sin C
Where, - Refractive Index C - Critical angle The four parameters on which angle of deviation depends are: 1. Angle of prism ( A ) 2. Material of prism ( ) 3. Angle of incidence ( I ) 4. Wavelength or color of light ( )
R ef r ac t i o n t h r o u g h Pr i s m : T h eo r y o n r e f ra c ti o n t h r o u g h P r is m :
When a ray of light passes from one medium into the other, it either bends towards the normal or away from the normal in the second medium, depending upon whether the second medium is denser or rarer with respect to first medium. This phenomenon is known as t h e R e fr a c t i o n o f l i g h t . For a particular pair of two media, and for a particular wavelength of light (colour) the ratio of the sine of the angle of incidence and the sine of the angle of refraction is a constant quantity called the Refractive Index of the second medium with respect to the first medium. It is represented by: =
Sin i -------Sin r
Therefore, the value of the angle of incidence i can be obtained in terms of the refracting angle A of the prism and the angle of minimum deviation m and the angle of refraction r can also be obtained in terms of the refracting angle A of the prism. Let ABC represent a section of the glass prism and let IP be a ray incident at angle i on the first face AB of the prism at a point P. N1PN is the normal to this face. The material of the prism is denser with respect to air, as such the ray will refract in the direction PQ making an angle r 1 with the normal reaching the second face AC of the prism at the point Q making an angle r2 with the normal N2QT. The ray emerging in the direction QE bending away from the normal and making an angle e with the normal. If the incident ray IP be produced backwards to meet QE produced at S, the angle KSQ is called the angle of deviation is
represented by D. Angle BAC is called the refracting angle of the prism and represented by A. To derive the relation: A+ D = i+e In
SPQ,
PS is produced to K. KSQ
D
or D is the external angle. =
SPQ
+
SQP
= i-r1 + e-r 2 = (i + e) - (r 1 + r 2) .............(1) r1 + r 2 + PTQ = 1800 r 1 + r2 = 1800 -
PTQ
.........(2)
Taking quadrilateral APTQ 0 0 0 APT + AQT = 90 + 90 = 180 A
+ PTQ = 1800
A
= 180 -
PTQ
----------------(3)
From (2) and (3) r1 + r2 =
A...........(4)
From (1) and (4)
D = i + e - A
A
+ D =
i+e
When the angle of deviation D has minimum value D m the following conditions are fulfilled: i = e and
r1 - r2 = r (say)
Applying these conditions in Eq.(2) and (3) A = 2 r A or r = ----...........(5) 2 and A + D m = 2 i A+Dm Or i = --------............(6) 2 Since u2
Sin i = -------Sin r
We obtain on substituting the value of (i) and (r) since
Sin(i) = -----------Sin (r)
Sin(A+Dm)/2 = ------------------------ .........(7) Sin(A/2) Thus we find that we can use the relation (7) for determining the refractive index. The experiment thus consists of finding of the value of the refracting angle of minimum deviation Dm. For finding the value of Dm a curve is plotted between the angles of incidence(1) and their respective angles of deviation (D).
PROCEDURE:
1. 2.
3. 4.
5.
6. 7.
8.
9.
Fix the sheet of white paper on Drawing board with cello tape or drawing pins. Draw a straight-line XY nearly at the center of the sheet parallel to its length. Mark points marked as O at suitable spacing on the line XY and draw normal to the line XY at point O. Draw straight line PQ corresponding to the incident rays that are drawn at the angles of incidence ranging from 30 to 60 i.e. for angles 35,40,45,50,55 & 60 using a protractor. Fill the liquid from open and of prism. Fix two pins P and Q about 8 cm on the incident rayline and view its image with one eye closed from the side of BC of the prism. Fix two pins R and S on the paper such that the tips of these pins and the tips of these images of the incident ray pins, all lie on the same straight line. Join the points (i.e. pin pricks) S & R and produce it backwards to meet the incident ray PQ produced. Thus RS is the emergent ray corresponding to the incident ray PQ. Draw arrow heads to show the direction of rays. Measure the angle of deviation D with Protractor. Repeat at steps (4 to 8) for different liquids having different values of angle of incidence and measure the corresponding 0 angles of deviation D. Take at least three values (i) from 30 to 400. Now place the prism on separate sheet of paper or on the same sheet at a suitable place and trace its triangular boundary with a sharp pencil. Measure the angle A, of the triangle so traced with the help of protractor. Record your observation in observation table.
Precautions
1.
A sharp pencil should be used for drawing the boundary of the prism.
2.
The separation between the pins should not be less than 8 cm. 3.
The angle of incidence should lie between 30-45.
4.
The same and prism should be used for all observations. So an ink mark should be placed on it to distinguish it as a refracting angle A of the prism.
5.
The pins should have sharp tips and fixed vertically and the pin pricks should be encircled immediately after they are removed.
6.
Proper arrow should be drawn to indicate the incident, the refracted and the emergent rays.
7.
A smooth curve passing practically through all the plotted points should be drawn.
OBSERVATIONS 1)
2)
FOR H2O:
Sl.No.
ANGLE OF INCIDENCE
ANGLE OF DEVIATION
1.
35o
25o
2.
40o
24o
3.
45o
23o
4.
50o
25o
5.
55o
26o
Sl.No.
ANGLE OF INCIDENCE
ANGLE OF DEVIATION
1.
35o
29o
2.
40o
26o
3.
45o
25o
4.
50o
27o
5.
55o
28o
FOR SPIRIT:
3)
For Glycerin:
4)
Sl.No.
ANGLE OF INCIDENCE
ANGLE OF DEVIATION
1.
35o
39o
2.
40o
38o
3.
45o
35o
4.
50o
40 o
5.
55o
41o
Sl.No.
ANGLE OF INCIDENCE
ANGLE OF DEVIATION
1.
35o
40o
2.
40o
39o
3.
45o
41o
4.
50o
42 o
5.
55o
45o
FOR BENZENE:
CALCULATIONS Formula Applied:Sin (A+Dm ) 2 = -----------------------
Sin (A/2)
1.
Water Sin (60+23 ) 2 =
= -----------------------
Sin(60/2)
Sin 30
=
2.
Sin(41.5) -------------------
0.6626 0.5
= 1.33
Spirit
Sin (60+25 )
2 = -----------------------
Sin(60/2) =
3.
0.6756
Glycerin
=
Sin 30 = 1.35 0.5000
Sin(42.5)
-------------------
Sin (60+35 )
2
Sin(47.5)
=
= -------------------------
Sin(60/2)
=
-------------------
Sin 30
0.7372 ---------
=
1.47 0.5
4.
Benzene
Sin (60+39 )
Sin(60/2) =
1.52
2 = -----------------------
Sin 30
=
Sin(49.5)
-------------------
Plotting of graph between i & D.
Plot a graph between angle i and D for various sets of values recorded in the observation table.
RESULT (i)
The angle of deviation D first decrease with the increase in the angle op-of incidence, attains a minimum value and then increase with further increase in angle of incidence.
(ii)
The refractive index of :i.
Water
= 1.33
ii.
Spirit
= 1.35
iii.
Glycerine
= 1.47
iv
Benzene
= 1.52
