Question

A concave lens has focal length of 20 cm. At what distance from the lens a 5 cm tall object be placed so that it forms an image at 15 cm from the lens? Also calculate the size of the image formed.

Answer 1

1/u=1/v -1/f

          = -1/15 +1/20

          =-4+3/60

           =-1/60

u=-60cm

H=v/u *h

 =-15/-60 * 5

=+1.25 cm
hope it helps u
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Answer 2

Hey Friend,

Applying the sign conventions according to concave lens - 
focal length (f) = - 20 cm
height of object (ho) = + 5 cm
image distance (v) = - 15 cm

Let the object distance be 'u' and height of image be 'hi'

Applying lens formula - 
1/f = 1/v - 1/u
1/u = 1/v - 1/f
1/u = 1/(-15) - 1/(-20)
1/u = 1/(-15) + 1/20
1/u = -4+3 / 60
1/u = - 1/60
u = - 60

Therefore, the object distance is - 60 cm.
The object should be thus placed at a distance of 60 cm from the lens.

magnification (m) = hi / ho = v / u

m = v/u 
m = -15 / -60
m = 1/4

m = hi/ho
1/4 = hi / 5
hi = 5/4
hi = 1.25 cm

Therefore, the size of image is 1.25 cm

Hope it helps!