Question

a concave lens of power - 2d is used to form an image of ana object of size 9 cm kept at a distance of 25cm from it find nature size and position of the image formed

Answer 1

given, power of concave lens , P = -2D

we know, power of lens , P = 1/f

so, -2D = 1/f => f = -50cm

size of object, $h_i$= 9cm

object distance from the lens , u = -25cm

using lens maker formula,

1/f = 1/v - 1/u

or, 1/-50 = 1/v - 1/-25

or, 1/-50 = 1/v + 1/25

or, 1/v = 1/-50 - 1/25 = 1/-50 - 2/50

or, v = -50/3 cm

hence, image formed 50/3 cm from the pole of lens on same side of object.

magnification, m = v/u

height of image/height of object = (-50/3)/(-50) =1/3

or, height of image/9cm = 1/3

or, height of image = 3cm

hence, image is virtual, erect and diminished.