INDEX
SL.NO T I T L E PAGE.NO
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2.
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10.
I n t r o d u c t i o n
Aim
Apparatus
Theory
Procedure
Diagram
Observation & calculation
Result
Precautions & source of error
Bibliography
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3
4
5
6
8
9
12
13
14
Introduction
Many optical tasks require several lenses in order to achieve an acceptable level of performance. One such possible approach to lens combination is to consider the image formed by each lens as the object for the next lens and so on. This is a valid approach, but it is time consuming and difficult. Liquid lens experiment can be used to find the optical constants of a lens and also to find the refractive indices of various liquids.
The theory behind the liquid lens is based on the properties of one or more liquid to create magnification within a small amount of space. The focus of a liquid lens is controlled by the surface of the liquid. Water normally form a bubble shape when adhered to materials like glass. Thos desirable property of water makes it a very suitable candidate for the production of liquid lens. Essentially the liquid must be transparent so as to study its properties. To generate a liquid lens, a liquid is sandwiched between two pieces of a clear plastic or glass. Glycerin can also be used as a fluid in the liquid lens system. The surface profiles of the liquid determine the focal length of the liquid lens system and how the liquid lens focuses the light rays.
If we keep the mirror behind the lens and put the object at the focus of the lens above it, the image of the object will be formed at the same focus where the object is. If it is an extended object, its image will be inverted and the size of the image is same as that of the object. This property has enabled the efficient use of liquid lens to find the refractive index of a fluid by this method. The focal length of the liquid lens can be calculated knowing the focal length of the combination and that of the convex lens, from which the refractive index of the fluid can easily be estimated.
AIM
To
determine:-1. Optical constants of a convex lens and
2. Refractive index of a liquid lens
.APPARATUS
1. The convex lens
2. Plane mirror,
3. The liquid
4. Glycerine
THEORY
Let f be the focal length andR
1and R
2be the radii of curvature of
a convex lens.
Then,
1
f
=
(n−1)(
1
R 1
+
1
R 2
)
Hence the refractive index n of the material of the lens is
n =
1+(
R 1 R 2)
f (R 1+R 2)
When the lens is placed over some drops of the given liquid on a
planmbination of the vconvex and the e mirror, a plano-concave liquid
lens is obtained. If F is the focal length of the combination of the
convex lens and the plano-concave liquid lens, the focal length of
the liquid lens is given by.
F
1=Ff
f −F
If the first face of convex lens is in contact with the liquid surface,
the radius of curvature of the upper surface of the liquid lens is R1.
For the liquid lens,
R1 = R1 & R2 =
∞
Hence
n
l =1+
R 1
f 1
PROCEDURE
To find the focal length of the convex lens
The convex lens is placed over a plane mirror which is
kept horizontally. A bright pointer O is arranged horizontally
on the clamp of a retort stand, vertically above the lens.
Looking from above, the pointer is moved up or down until the
pointer and its inverted image coincides without parallax. The
distance x1 and x2 of the pointer from the top of the lens are
measured. The average distance[x1+x2]/2 gives the focal
length f of the convex lens. The experiment is repeated and
the mean focal length is calculated.
To find the focal length of the liquid lens
The lens is then removed, a few drops of the given liquid placed
on the plane mirror. The lens is placed on it with the marked
first surface of the lens in contact with the liquid. The liquid
lens forms a plano-concave lens. The pointer is arranged
horizontally above the lens. Looking from above, the pointer is
moved up or down until the pointer and its inverted image
coincides without parallax. The distances x1 and x2 are
measured as before. The average distance[x1+x2]/2 gives the
focal length f1 of the combination of the convex lens and liquid
lens. The focal length f1 is calculated from the equation
F
1=Ff
f −F
Repeat the experiment by keeping the second surface on water
and determine f2
And find R
2andR
2by Using formula
1
f
=
1
R 1
+
1
R 2
(
n−1)
¿
)
Find the focal length f for glycerine
Few drops of glycerine is added on a mirror. Lens is placed upon
it such that it formed a plano-concave lens. The pointer is
arranged horizontally to get a coinciding object and image
without parallax. Distances x1 and x2 are noted as before.
Focal length is calculated by using formula
f =
x 1+ x 2
2
.
DIAGRAM
Fig: liquid lens apparatus.
Fig: To find radius of curvature of lens
(i)To find focal length of lens
Sl.no Distance of pointer from
Focal length (cm) T o p o f l e n s (cm) T o p o f m i r r o r (cm) 1 2 3 4 5 10.1 10.2 9.9 10 10.3 11.1 11.2 10.9 11 11.3 10.6 10.7 10.4 10.5 10.8 Mean = 10.6 cm
(ii) To find the focal length of the combination, 1st surface
Sl.no Distance of pointer from
Focal length (cm) T o p o f l e n s (cm) T o p o f m i r r o r (cm) 1 2 3 4 5 15 15.2 14.8 15.3 15.4 16 16.2 15.8 16.3 16.4 15.5 15.7 15.3 15.8 15.9 Mean focal length of combination,
Focal length of combination , surface 2
Sl.no Distance of pointer from
F o c a l l e n g t h (cm) T o p o f l e n s (cm) T o p o f m i r r o r (cm) 1 2 3 4 5 15.5 15.1 15.3 15.0 15.6 16.5 16.1 16.3 16.0 16.6 16.0 15.6 15.8 15.5 16.1 Mean focal length, = 15.8 cm
F1 = 15.64 cm F2 = 15.80 cm We know,
1
f
=
1
R 1
+
1
R 2
(
n−1)
¿
)
R1= (n–1) f1 (R2=∞
) = 15.64 ( 1.33 – 1) (n= 1.33 for ) = 15.64 (1.33 – 1) = 5.161 cm Similarly , R2= (1-n) f2 = 15.8 × 0.33 = 5.214 cmAlso
f
1=Ff
f −F
=15.576 cm
(iii) Focal length of liquid lens using glycerin
Sl.no D i s t a n c e o f p o i n t e r f r o m Focal l en gth (c m ) T o p o f l e n s (cm) T o p o f m i r r o r (cm) 1 2 3 4 5 1 9 . 6 19.5 19.0 19.2 19.4 2 0 . 6 20.5 20.0 20.2 20.4 2 0 . 1 20.0 19.5 19.7 19.9 Mean focal length of glycerin lens = 19.84 cm
CALCULATIONS
