Abstract
As a concave lens always forms a virtual image, its focal
length cannot be found directly as for a convex lens. For this purpose,
indirect method is used, as described below.
An object needle O is placed on one side of a convex lens L_{1}
and its real inverted image I is located (by image needle) on the other side as
shown in ray diagram.
The concave lens L_{2} is placed between convex lens
L_{1} and image needle I. The concave lens diverges the rays and the
image is now formed at l' as shown in ray diagram.
For concave lens, I is the virtual object and I' is the real
image. Hence, O₂l = u and O₂l' = v.
Focal length can be calculated, using lens formula,
`1/f` = `1/v  1/u`
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
 Convex lens and
 Concave lens.
Convex lens
The distance between the principal focus and the centre of the lens is called the focal length [3].
Concave 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].
Auxiliary lens
Theory
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)
`P` = `100/f (cm)` … … … … … … … … … … … … (2)
Apparatus
 Optical bench
 Concave lens
 Convex lens
 Screen
 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 DDiscussion
Conclusion
References
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