Experiment Name:
To Determine the Refractive Index of a Liquid by Pin Method Using a
Plane Mirror and a Convex Lens.
Theory: If a convex lens is placed
on a few drops of liquid on a plane mirror, then on squeezing the liquid into
the space between the mirror and the lens a Plano-concave liquid lens is
formed. The curved surface of this liquid lens has the same radius of curvature
as the surface of the convex lens with which it is in contact. Thus we have a
combination of two lenses –one of glass and the other of liquid, which behaves
as a convergent lens. If F be the focal length of the combination then
= 
+
. . . . . . . . . . . . . (1)
Where f1 and f2
are the focal lengths of the convex lens and Plano-concave liquid lens
respectively.
Sign of the Plano-concave
liquid lens ( f2 ) is negative.So,We get
Or, 
= 
=
Or, f2 = 
. . . . . . . . . . . . . .(2)
. . . . . . . . . . . . . .(2)
The focal length f2 of the
plano-concave liquid lens is also given by the relation
= (µ-1) ( 
)
Or, = (µ-1) ( 
[r´=α, the lower face of the
liquid lens being a plane)
= (µ-1) ( [r´=α, the lower face of the
liquid lens being a plane)
Or, µ - 1 = 
( sign convention, both f2 and
r are negative)
( sign convention, both f2 and
r are negative)
Or, µ = 1 + 
. . . . . . . . . . . . .(3)
. . . . . . . . . . . . .(3)
Where µ is the
refractive index of the liquid.
Again, the radius of curvature of the
spherical surface is given by
r = 
+ 
…………………………….(4)
+
…………………………….(4)
Where a is the mean distance betn
the outer legs of the spherometer and h the height of the central leg above or
below the plane through the tips of the outer legs.
From equation (2), (3) & (4) we get
refractive index ( µ ) of the liquid.
Apparatus:
A convex lens, plane mirror, pin
with its tip painted red, speedometer, slide calipers, stand and some
experimental liquid.
Procedure:
1. The plane mirror is placed on
the base of the stand with the pin held horizontally by the clamp above see
figure 1.
2. The convex lens is then placed
on the mirror, and its focus is found by locating the position of the pin where
it coincides with its own image. By measuring from this point to the lens, its
focal length (f1) is found.
3. The lens is now removed, and a
few drops of liquid are placed on the mirror. On placing the convex lens on the
liquid, a combination of a convex (glass) and a Plano-concave (liquid) lens
results.
4. The focal length (f) of the
combination is found as above, and the focal length (f2) of the liquid lens
calculated from f and f1 equation (1).
5. The radius of curvature (r) of
the lens surface in contact with the liquid is now obtained by a spherometer ,
or by boys, method.
6. Calculate the refractive index
of liquid from equation (3).
Data Collection:
(A). Calculation of the
least count.
Pitch (P) = 
No. of divisions in the circular scale, n = 100
Least count
(L.C): = 
= mm
= cm
(B). Measurement of h:
|
Reading No.
|
No.
of obs.
|
Linear Scale Reading
(x)
|
Circular Division
(CD)
|
Least Count
(LC)
|
Total Reading
= X + C.D X
L.C
|
Mean
Reading
|
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|
|
cm
|
|
cm
|
cm
|
cm
|
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Base plate
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Lens surface
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h = (Reading
on lens – Reading on base plate) cm
= cm
(C). Measurement
of a:
a1 = cm. a2= cm a3
= cm
Mean a = cm
Hence the radius of curvature of
the spherical surface,
r =
+
=
cm
+
=
cm
(D)Thickness
of the lens:
t = MSR + V.S × V.C =
cm
(D). Determination of the focal lengths:
|
No
of
obs.
|
Distance betn
the pin and the face of the lens without liquid
h1
|
Focal length
of the convex lens
f1 =h1+
 |
Mean
Focal length
f1
|
Distance betn
the pin and the top surface of the lens with liquid
h2
|
Focal length
of the combination
F = h2
+
 |
Mean
Focal length
F
|
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cm
|
cm
|
cm
|
cm
|
cm
|
cm
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01
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02
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03
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Calculation: From equation (2) and (3), we get
f2 = 
cm
cm
= cm
= cm
And
µ = 1 +
=
=
Result: The refractive index of the
liquid (water) is………………………..
Percentage of error: 
X 100%
X 100%
=
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