In the displacement method , a convex lens is placed in between an object and a screen . If one of them magnification is 3 and the displacement of the lens between the two positions is 24 cm , then the focal length of the lens is :-

Options

A. 10 cm
B. 9 cm
C. 6 cm
D. 16/3cm

Answer

B

Explanation

`X = u_(2) - u_(1) = 24`
`m = (v_(1))/(u_(1)) = 3 implies v_(1) = 3u_(1) "or" u_(2) = 3u_(1)`
`3u_(1) - u_(1) = 24 implies u_(1) = 12 "cm"`
Hence `f = (D^(2) - X^(2))/(4D) = ((48)^(2) - (24)^(2))/(4 xx 48)`
=`((48 +24) (48-24))/(4 xx 48) = (72 xx 24)/(4 xx (48)^(2)) = 9 "cm"`