The image of a needle placed `45 cm` from a lens is formed on a screen placed `90 cm` on the other side of lens. Find displacement of image if object is moved `5 cm` away from lens.

Options

A. `10 cm`, towards the lens
B. `15 cm,` away from the lens
C. `15 cm`, towards the lens
D. `10 cm`, away from the lens

Answer

C

Explanation

Here, `u = -45 cm, v = 90 cm`
`:. (1)/(f) = (1)/(v) - (1)/(u) = (1)/(90) + (1)/(45) = (1)/(30) rArr f = 30 cm`
when the needle is moved `5 cm` away from the lens,
`u = - (45+5) = - 50 cm`
`:. (1)/(v') = (1)/(f) + (1)/(mu') = (1)/(30) + (1) /((-50)) = (2)/(150) rArr sqrt() = 75 cm`
Displacement of image `= v -v' = 90-75 = 15 cm`, towards the lens.