Question

size of the image of an object by a concave lens of focal length 20cm is observed to be reduced to 1/2 of its size. find the distance of the object from the lens.​

Answer 1

Explanation:

$f = 20cm \\ m = \frac{v}{u} = \frac{1}{2} \\ = > u = 2v$

By Lens formula,

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ = > \frac{1}{20} = \frac{1}{v} - \frac{1}{2v} \\ = > \frac{1}{20} = \frac{2 - 1}{2v} \\ = > \frac{1}{20} = \frac{ 1}{2v} \\ = > v = 10 \: cm \\ = > u = 20 \: cm$

Hence, the distance if the object from the lens= 20 cm

Answer 2

hi mate,

Solution: object distance from the optical centre of the lens is 40cm.

explanation : focal length of concave lens , f = -20cm

a/c to question,

size of image = 1/3 × size of object.

so, magnification , m = 1/3

we know, magnification of lens , m = v/u

so, v/u = 1/3

so, v = u/3 ........(1)

now applying lens maker formula,

1/v - 1/u = 1/f

or, 1/(u/3) - 1/u = 1/-20

or, 3/u - 1/u = 1/20

or, 2/u = 1/-20 cm

or, u = -40 cm

hence, object is placed 40cm from the pole of concave lens.

i hope it helps you.......

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