A lens form a diminshed and erect image of an object. The magnifiation is `(1)/(4)`. Find ratio of distances between object and focus and focus and image:

Options

A. `4:1`
B. `1:4`
C. `8:1`
D. `2:1`

Answer

c.

Explanation

The lens is concave `m=(v)/(u)=(1)/(4)=(x)/(4x)`
Distance between object and image `=3x`
`(1)/(f)=(1)/(v)-(1)/(u)=-(1)/(x)+(1)/(4x)rArr f=-(4x)/(3)`
Distance between object and focus `= 4x-(4x)/(3)=(8x)/(3)`
Distance between image and focus `=(4x)/(3)-x=(x)/(3)`
Thus, required ratiois `8:1`
See the diagram, `(OF)/(Fl)=(8)/(1)`