When an object is placed on the principal axis of a convex lens at two different positins, it produces the images with magnifications `+2` and `-4` respectively. How many times more away from the lens the image will be formed in the second position as compared to the first postion?

Options

A. 2
B. 4
C. 5
D. 10

Answer

c.

Explanation

`m=+2,u=-x`
`v=-2x`
`-(1)/(2x)+(1)/(x)=(1)/(f)` (i)
Similarly, `m=-4, u=-y, and v=+4y`
`(1)/(4y)+(1)/(y)=(1)/(f)` (ii)
Equating (i) and (ii), `(1)/(2x)=(5)/(4y)`
`x=0.4y` or `y =2.5x`
Required ratio of images `=4y:2x`
`=(4)(2.5):2x=5:1`