Question

a lens of focal length 20 cm is used to produce a ten times magnified image of a film slide on a screen. How far must the slide be placed from the lens

Answer 1

focal length = f = 20 cm
object distance = - u
image distance = v
magnification = m = -10 [- sign is used because the image is real since it is obtained on screen]

we know, m=v/-u
-10 = v / -u
10 u = v

using,
1/f = 1/v - 1/-u
1/20 = 1/10u + 1/u
1/20 = 1+10 / 10u
10 u / 20 = 11
u = 22 cm

therefore, the object distance is 22 cm

now v=10x22 = 220 cm

Answer 2

Given, F=20cm m= -10 ( because only real image can be obtained on a screen)

-10=v/u = -10u=v

Applying lens formula

1/v-1/u=1/f

So, 1/-10u - 1/u = 1/20

This gives -1-10/10u = 1/20

-11*20 =10u

So u= -22cm