CERTIFICATE This is to certify that …………………………...... of Class XII-A
has
completed
the
Physics
project
titled
“REFRACTIVE INDICES OF VARIOUS LIQUIDS” in partial fulfilment of curriculum of ALL INDIA SENIOR SECONDARY EXAM (CBSE). This project was carried out in the school laboratory of K.V. Pangode during the academic year 2014-15.
Internal Examiner
External Examiner
School Seal
Principal 1
Acknowledgement I take this opportunity to express my gratitude in few words and respect to all those who helped me in the completion of this project. The successful completion of any task would be incomplete without mentioning the names of those persons who helped to make it possible. It is my humble pleasure to acknowledge my deep senses of gratitude and heartfelt indebtedness to my teacher Smt.Lekshmi Devi for her valuable support, constant help and guidance at each and every stage, without which this project would not have come forth. I also register my sense of gratitude to our Principal, my teacher Shri K. B. K Unnithan, for his immense encouragement that has made this project successful. I would also like to thank my friends and family for their endless support without which I could not have completed this work in time. 2
INDEX Sl no:
Title
Page no:
1.
Certificate
02
2.
Acknowledgement
03
3.
Introduction
05
4.
Experiment
13
5.
Bibliography
23
3
Introduction This project envisages the use of hollow glass prism to calculate the refractive indices of various liquids. The hollow glass prism is filled with the liquid and then the deviation in the path of the ray of light, as it suffers refraction, is studied. Readings of the experiment are noted with the various liquids and refractive index is calculated for each pair of media.It has been assumed that the refractive index of the liquids is with respect to that of air.Important general terms related to refraction of light are given below:Refraction: In a homogenous medium, light travels along a straight line. But whenever it falls on the 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 two media is called refraction of light. 4
Cause of Refraction: The phenomenon of refraction takes place when a beam of light enters a medium in which light travels with a different velocity. Laws Of Reflection: 1. The reflected ray, the incident ray, and the normal at the point of incidence all lie in the same plane. 2. The angle of incidence is equal to the angle of reflection. Laws Of Refraction: 1.The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane. 2.For any two given media the ratio sin i / sin r is a constant (where i is the angle of incidence, r is the angle of refraction). This is also called Snell's Law. Refractive Index:
5
For a monochromatic light, the ratio of the sine of the angle of incidence to the angle of refraction is a constant for two given media in contact.If "i" is the angle of incidence and "r" the angle of refraction then sin i / sin r = constant.
6
This constant is called the refractive index. For most purposes it may be assumed that the refractive index is w.r.t. air. When light travels from rarer to denser medium it bends towards the normal and when it travels from denser to rarer medium it bends away from the normal. It has been experimentally determined that refractive index of a substance, µ= c/v. c=the speed of light in vacuum v= the speed of light in the substance
7
Prism: A portion of transparent medium bounded by two
plane surfaces inclined to each other at a suitable angle is called a prism. The angle between the two faces is known as the angle of the angle of the prism or the refracting angle.
Refractive Edge: The line of interaction of the edges of the planes is known as the refractive edge of the prism. Angle of Deviation: The angle through which the incident ray of light is deviated is called the angle of deviation. It is the angle 8
between the emergent ray and the incident ray produced.
Angle of Minimum Deviation: As the value of the angle of incidence (i) increases, the angle of deviation (d) decreases till for a particular value of angle of incidence, it attains a minimum value 'Dm' called the angle of minimum deviation and then increases again. At this angle (Dm) the incident ray and the emergent ray are symmetrical w.r.t. the refracting surfaces. Critical Angle: It is that angle of incidence in the denser medium for which the corresponding angle of refraction in the rarer medium is 90 degrees.
µ = l/sin c where
µ = Refractive Index 9
c= critical angle Relation between refractive index and critical angle according to Snell's Law: b
b
µa= sin i/ sin r where i = c and r = 90°
µa = sin c/ sin 90° = sin c
But
b
µa = 1/ aµb
i.e. 1/ aµb = sin c or aµb= 1/sin c PRISM FORMULA
10
Let ABC represent a section of the glass prism and let L be a ray incident at an angle "I" on the first face AB of the prism at a point "E". NN’ is the normal to this face. The material of the prism is denser with respect to air, as such the ray would refract in the direction EF making an angle r with the normal, reaching the second face AC of the prism at the point F making an angle e with the normal MM’ . The ray emerges in the direction FS bending away from the normal making an angle "e" with the normal. If the incident ray PE be produced forwards to meet FS (also to be produced backwards) at G then the angle HGF is called the angle of deviation and is represented by D. Angle "BAC" is called the refracting angle of the prism and represented by "A". 11
From the figure it can be proved: D = (I + e) - (r1 + r2) (using exterior angle property of a triangle) and A = (r1 + r2) Therefore A + D = I + e; when angle of deviation D has the minimum value Dm, the following conditions are fulfilled I = e and r1 = r2 = r (say) Applying these conditions in the equation A = 2r Or r = A/2 A + Dm = 2I I = (A + Dm)/2 Since 1µ2 = sin i/ sin r 1
µ = {sin(A + Dm)/2}/{sin A/2}
12
Experiment AIM: To find out the refractive indices of different liquids using a hollow prism and to find the speed of light in given transparent fluids.
APPARATUS:
Hollow glass prism Drawing board Pins Meter scale Protractor Sheets of white paper Various liquids a) Glycerine b)Water c) Vinegar d)Vegetable Oil
THEORY: Light is an electromagnetic radiation that is visible to the human eye usually having a wavelength in the range of 400 nm to 700 nm between the infrared, with longer wavelengths and the ultraviolet with the shorter wavelength. The speed of light in vacuum is found to be
exactly 299,792,458 m/s. Observable events that result from the interaction of light and matter are called optical phenomenon. Refraction is a surface phenomenon due to a change in its transmission medium.
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. This phenomenon is known as the refraction of light. A prism is a transparent optical element with flat, polished surfaces that refract light. Prisms can be made from any material that is transparent including glass, plastic and fluorite. A prism can be used to break light up into its constituent spectral colors. Prisms can also be used to reflect light, or to split light into components with different polarizations.
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 w.r.t. the first. It is represented by ----- 2µ1 = sin i / sin r.The value of the angle of incidence "i" can be obtained in the terms of the refracting angle "A" of the prism and the angle of minimum deviation "Dm" and the angle of refraction "R" can also be obtained in terms of the refracting angle "A" of the prism. Thus we find that we can use the above relation derived for determining the refractive index. The experiment thus consists in finding the value of the refracting angle "A" of the prism and the value of the angle of minimum deviation Dm. The refractive index of the liquid Is given by the formula: µ = {sin(A + Dm)/2}/{sin A/2} For finding the value of Dm a curve is plotted between
angles of incidence (i) and their respective angles of deviations (d).
PROCEDURE A) For finding the angle of prism Take a piece of white paper, fix it on a drawing board using board pins. Place the hollow glass prism on the sheet and carefully draw its outline. Draw a normal and carefully draw its outline. Draw a normal and an incident ray at an angle of 35 degrees with the normal on side AB of the prism. Fix two pins P1 and P2 on the incident ray which are at least 5 cm apart. Fill the prism with water and place it over its outline. Observe the refracted ray that comes after refraction from the face AB of the prism. Fix two more pins P3 and P4 to cover the image of P1 and P2. Obtained angles r1 and r2 and add them to obtain the angle of the prism. B) For finding the angle of minimum deviation Fix a white sheet of paper on a drawing board using board pins
Place a hollow glass prism on the sheet and carefully draw its outline. Draw a normal and an incident ray of angle of incidence 35 degrees on the side AB of the prism. Fix two pins P1 and P2 on the incident ray at least 5 cm apart. Fill the hollow prism with water and place it over its drawn outline. Observe the refracted ray which comes after refraction by placing two more pins P3 and P4 covering P1 and P2. Extended the incident and refracted ray to obtain the angle of deviation, D. Repeat the above procedure taking other liquids and the angles of incidence as 40° , 45° , 50° , 55° and 60°. Note the lowest obtained value of angle of deviation as the angle of minimum deviation, Dm . Using the value of the angle of prism (A) and the angle of minimum deviation (Dm), calculate the value of the refractive index of the liquids by using the equation given in the theory. Select suitable scales to represent the angle of incidence along the X-axis and angle of deviation along
the Y-axis and plot a graph. The graph gives the value of Dm, which is the minimum most point of the parabola. S.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Name of Liquid
Water
Vinegar
Vegetable Oil
Glycerine
OBSERVATIONS:
Angle of
Angle of
Incidence Deviation 35° 40° 45° 50° 55° 60° 35° 40° 45° 50° 55° 60° 30° 35° 40° 45° 50° 55° 35° 40° 45° 50° 55° 60°
25° 24° 23° 25° 27° 28° 26° 25° 23.5° 25° 27° 28° 49° 40° 39° 34° 36° 39° 41° 38° 36° 35° 36° 38°
CALCULATIONS: A) Refractive index of liquids Angle of prism (A) = 60° Formula used: µ= {sin ((A + Dm)/2}/{sin (A/2)} Water: Dm=23° Therefore µ =
sin 41.5 0.6626 = =1.3252 sin 30 0.5
Vinegar: Dm=23.5° sin 41.25 0.6593 = =1. sin 30 0.5
Therefore µ =
3186
Vegetable Oil: Dm=34° Therefore µ =
Glycerine:
sin 47.0 0.7314 = =1.4628 sin 30 0.5
Dm=35° Therefore µ =
Sl no 1 2 3 4
sin 47.5 0.7373 = =1.4746 sin 30 0.5
Speed of light v= Liquid Water Vinegar Vegetable oil Glycerine
c n
Speed of light
(m/s)
3×10 /1.3252 3×108/1.3186 3×108/1.4626 3×108/1.4726 8
(m/s) 2.26×108 2.27×108 2.05×108 2.03×108
B) Speed of light in liquids
Graph for angle of minimum deviation
RESULT The refractive indexes of the four liquids were found to be as follows:
Water, µ = 1.3252 Vinegar, µ = 1.3186 Vegetable Oil, µ = 1.4628 Glycerine, µ = 1.4726
The speeds of light in the four liquids were found to be as follows:
Water, v=2.26×108 m/s Vinegar, v=2.27×108 m/s Vegetable oil, v=2.05×108 m/s Glycerine, v=2.03×108 m/s
PRECAUTIONS
The position of the prism should not be disturbed on the white sheet. There should be no parallax between the pins P1, P2 and their images P3, P4. The angles should be measured carefully. The curve of the graph should be smooth.
SOURCES OF ERROR Pin pricks may be thick Measurement of angles may be wrong
BIBLIOGRAPHY Physics Class XII NCERT Textbook Comprehensive Practical Physics by Lakshmi Publications www.hyperphysics.com Google images
