A piece of wire bent into an L shape with upright and horizontal portion of equal lengths 10 cm each is placed with the horizontal portion along the axis of the concave mirror towards pole of mirror whose radius of curvature is 10 cm. If the bend is 20 cm from the pole of the mirror, then the ratio of the lengths of the images of the upright and horizontal portion of the wire is

Options

A. `1:2`
B. `3:1`
C. `1:3`
D. `2:1`

Answer

b.

Explanation

For upright portion,
`m=(f)/(f-u)=((-10)/(2))/((-10)/(2)-(-20))=(-5)/(-5+20)=(-5)/(15)=-(1)/(3)`
For horizontal portion, magnification is `(-(1)/(3))^(2)` i.e., `(1)/(9)`
Required ration is `(-1//3)/(1//9)=-3:1`