A convex lens produces an image of a real object on a screen with a magnification of 1/2. When the lens is moved 30 cm away from the object, the magnification of the image on the screen is 2. The focal length of the lens is

Options

A. 30 cm
B. 60 cm
C. 20 cm
D. 15 cm

Answer

C

Explanation

(c ) In the first case, let
u=-x
Then, `v=+x/2`
`therefore 2/x+1/x=1/for3/x=1/f`
In the secon case,
`u=-(x-30) rArr v=2(x-30)`
`therefore 1/(2(x-30))+1/(x-30)=1/f=3/x`
On solving Eqs. (i) and (ii), we get
f=20 cm