AIM To find
refractive indices of liquids by using an equiconvex
lens and a plane mirror.
EQUIPMENT REQUIRED
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An equiconvex lens
A plane mirror
Clean transparent liquid in a beaker
An optical needle
An iron stand with base and clamp arrangement
Plumb line
Spherometer
• Half meter scale
BASIC
PRINCIPLE
Refractive Index:
In optics, the
refractive index n of a substance (optical medium) is a dimensionless
number that describes how light, or any other radiation, propagates
through that medium. It is defined as
where c is the speed of light in vacuum and v is the speed of light in
the substance. For example, the refractive index of water is 1.33,
meaning that light travels 1.33 times as fast in vacuum as it does in
water. The historically first occurrence of the refractive index was in
Snell's law of refraction, n1sinθ1= n2sinθ2, where θ1 and θ2 are the
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angles of incidence of a ray crossing the interface between two media
with refractive indices n1 and n2.
Lens Maker’s Formula: It is a relation that connects focal length of
a lens to radii of curvature of the two surfaces of the lens and refractive
index of the material of the lens.
The following assumptions are made for the derivation:
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The lens is thin, so that distances measured from the poles of its
surfaces can be taken as equal to the distances from the optical
centre of the lens.
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The aperture of the lens is small.
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Point object is considered.
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Incident and refracted rays make small angles.
P = 1/f = (n-1){ 1/R1 – 1/R2}
THEORY
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If f1 and f2 be the focal length of a glass convex lens and liquid
lens and F be the focal length of their combination, then,
1/F = 1/f1 +1/f2 OR 1/f2 = 1/F – 1/f1
Liquid lens formed is a Plano concave lens with R1=R (radius of
curvature of convex lens surface), R2 = ∞. From lens maker’s
formula:
1/f2 = (n-1) [1/R1 – 1/R2]
Therefore, 1/f2 = (n-1)/R OR n = 1+ R/f2
On substituting the value of f2, n refractive index (n) can be
calculated.
PROCEDURE
(a) For focal length of convex lens:
1. Take any one convex and find its rough focal length.
2. Take a plane mirror and place it on the horizontal base of the iron
stand.
3. Place the convex lens on the plane mirror.
4. Tighten the optical needle in the clamp of the stand and hold it
horizontally above the lens at distance equal to its rough focal
length.
5. Bring the tip of the needle at the vertical principle axis of the lens, so
that the tip of the lens appears to be touching the tip of the image.
6. Move the needle up and down to remove parallax between the tips
of the needle and its image.
7. Measure the distance between the tip of the needle and the upper
surface of the lens by using a plumb line and a half meter scale.
8. Record your observations in the observations table. (b) For focal
length of the combination:
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1. Take a few drops of transparent liquid on the plane mirror
and put the convex lens over it (A Plano convex liquid lens
is formed between plane mirror and convex lens.).
2. Move the needle up and down to remove parallax between
the tips of the needle and its image.
3. Measure the distance between the tip of the needle and the
upper surface of the lens by using a plumb line and a half
meter scale.
4. Record your observations in the observations table.
(c) For radius of curvature of convex lens surface:
1. Raise the central screw of the spherometer and press the
spherometer gently on a sheet so as to get the marks of the
three legs. Mark these points as A, B and C.
2. Measure the distance between these points and take their
mean.
3. Find the value of one vertical (pitch) scale division, 4.
Determine pitch and least count of the spherometer.
5. Place the spherometer on the convex lens surface and turn
the screw turn the screw tip just touches the convex surface.
6. Note the reading of the circular scale which is in line with
the pitch (vertical) scale.
7. Now place the spherometer on a plane glass slab.
8. Turn the screw downwards and count the number of the
complete rotations made by the disc.
9. Continue till the tip of the screw just touches the plane
surface of the slab.
10. Note the reading of the circular scale which is in line with
the pitch (vertical) scale.
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11. Repeat the experiment two more times and record the
observations.
DIAGARAM AND EXPERIMENTAL SET UP
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OBSERVATIONS
CALCULATIONS
Rough focal length of convex lens =10.4cm
1. Calculation for Refractive Index of water 1/F=1/f1+1/f2
1 1 10.4 = f2 15.55
1 =-0.03184
f2-31.407cm
Or
1/f2=1/F-1/f1
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1/f2 - 1/(15 * 55) - 1/10.4
1/f2 - 1/(15 * 55) - 1/10.4
f2= - 31.407cm
Now taking out Refractive Index
R n=1+R/2
But, R= fid/f₁-d
R=( 10.4×5.91) / (10.4-5.91)
R=-13.73cm
n=1+ (-13.73)/ (-31.407)
n=1+ 13.73/ 31.407.
n = 1+0.437
n = 1.437
Percentage Error=Actual Value-Observed Value x 100
Actual Value= (1.33 – 1.43)/1.33 * 100= 0.1/1.33 * 100
= 7.51 \%
2.Calculation for Refractive Index of oil
1/F = 1/f1 + 1/f2
1/f3 = 1/F – 1/f_3
1/f2 = 1/18.8 – 1/10.4
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1/f2 = - 0.043
F2 = - 23.255cm
Now taking out Refractive Index
N = 1 + R/f2
But, R = (f1*d)/(f1 – d)
R = (10.4 * 6.024)/(10.4 – 6.024)
R = - 14.32cm
N = 1 + (- 14.32)/(- 23.255)
N = 1 + 14.32 23.255
N = 1+0.615
N = 1.615
Percentage Error Actual= Value-Observed Value X 100
Actual Value=1.56-1.615 1.56 X 100
=0.055 1.56 X 100
= .0352 x 100 = 3.52%
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RESULTS
Refractive Index of water = 1.437
Percentage error of water = 7.51%
Refractive Index of coconut oil = 1.615
Percentage error of coconut oil = 3.52%
CONCLUSION
The experimentally determined values and theoretical values of
the refractive indices of the liquids concerned are the same within
the limits of error.
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BIBLIOGRAPHY
1. http://www.abhinav.ac.in/DoV/Labs/P/XI_P_Set2.p
df
2.
3. http://uotechnology.edu.iq/deplaserandoptoeleceng/
laboratory 4.
4. http://en.wikipedia.org/wiki/Refractive_index
5.
5. Physics lab manual, Comprehensive Practical
6.
Physics for class XI and XII
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