Abstract
Introduction:
A
lens is a transmissive optical device that focuses or
disperses a light beam by means of refraction. A simple lens consists of a
single piece of transparent material, while a compound lens consists of
several simple lenses (elements), usually arranged along a common axis [1].
Lens are
generally mainly two in number. They are
1. Convex lens and
2. Concave lens.
A lens is biconvex (or double convex,
or just convex) if both surfaces are convex.
If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave
surfaces is biconcave (or
just concave). If one of the surfaces is flat, the lens is planoconvex or planoconcave depending on the
curvature of the other surface. A lens with one convex and one concave side is convexconcave or meniscus [2].
Fig. 01 (types of lens)
Concave lens: Convex
lenses are thicker at the middle. Rays of light that pass through the lens are
brought closer together (they converge).
A convex lens is a
converging lens. When parallel rays of light pass through a
convex lens the refracted rays converge at one point called the principal
focus.
The distance
between the principal focus and the centre of the lens is called the focal
length [3].
Fig. 02 (convex lens)
Concave lens: Concave
lenses are thinner at the middle. Rays of light that pass through the lens are
spread out (they diverge). A concave lens is a diverging lens.
When parallel rays
of light pass through a concave lens the refracted rays diverge so that they
appear to come from one point called the principal focus.
The distance
between the principal focus and the centre of the lens is called the focal
length.
The image formed
is virtual and diminished (smaller) [4].
Fig. 03 (concave lens)
Auxiliary lens: a lens attached to an objective to change its focal length. A positive lens decreases the focal length,and a negative lens increases it. Positive lenses are used for largescale photography (macrophotography) with still and motion picture cameras, in which extension of the lens toward the object being
photographed is limited.
The
concave lens can not produce a real image of a real object; but if a virtual
object is placed within its focus, it can produce a real image of the virtual
object. This principle is utilized in determining the focal length of a concave
lens. At first a real image of a real object is produced with the help of a
convex lens. Then a convex lens is interposed between the convex lens and its
real image in such a way that the real image falls within the focus of the
concave lens.
Theory:
From
lens formula,
We
have,
…
… … … … … … … … … … … (1)
Where, f = focal
length of concave lens L_{2}
U = distance of I from
optical centre of lens L_{2}
V = distance
of Iꞌ from optical centre of lens L_{2}
(Note. According to sign convention, u and v have positive values (being
measured in direction of incident
light. v < u, u – v is negative. Hence f
comes
negative)
And ,
…
… … … … … … … … … … … (2)
Where, P = power
f = focal length.
Apparatus:
1. optical bench
2. concave lens
3. convex lens
4. screen
5. index rod etc.
Experimental data:
No
Of
object

Position of

Apparent
Object
distance
U=L~P

Apparent
Image
distance
V=L~I

U=
U`+λ

V=
V`+ λ


Object
(o)

Convex
Lens (p)

Image with convex lens(p)

Concave lens (L)

Image with combination
(I)


1

0

17

37

28.5

42

8.5

13.35

8.9

13.9

2

0

17

37

26

47

13

21

13.4

21.4

3

0

17

37

24.2

52

15

28

15.4

28.4

4

0

17

37

23.7

57

13

33.3

13.7

33.7

Table: determining of ‘f’
No
Of
object

Object distance
(v)

Image distance (v)

Focal length

Mean focal length (f) cm

Power,(p)
=100/f(cm)
diopter

1

8.9

13.9

24.742

26.82

3.728

2

13.4

21.4

25.845


3

15.4

28.4

33.643


4

13.7

33.7

23.084

Table for index error ( λ ) between convex lens &
screen
Length
index rod (cm) l

Diff.
of bench scale reading in cm when the two ends of the index rod touch the
concave lens & screen

Index
correction in cm λ =(ld)

30.3

29.9

0.4

Calculation:
Focal length ,
Percentage
of error:
Result:
The focal length of the
given concave lens is 26.82 cm. with an
error of 7.28% and power is
3.728 D
Discussion:
The image formed by the
concave lens was focused on the screen by shifting the positions of the concave
lens and not by moving the screen. This is necessary because the focused
condition of the image would not change within an appreciable range of the
movement of the screen.
The light emerges from
the concave lens parallel to the axis and consequently no image is formed when
LP is equal to the focal length of the concave lens.
Knowing the distances
of an object and distance of image formed, we can calculate every accurate
focal length. Our focal length were not very close enough and especially the
first is too small. However those readings were taken more carefully and
accurately.
Conclusion:
In
this experiment we had determined the focal length of given concave lens and
its power. During experiment, it was necessary to take position of lens by a
distance of 4f for concave lens.
References:
[3].
http://www.passmyexams.co.uk/GCSE/physics/concavelensesconvexlenses.html
[4]. http://www.passmyexams.co.uk/GCSE/physics/concavelensesconvexlenses.html
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##MIST (Military Institute of Science and Technology)