A `10 mm` long awl pin is placed vertically in front of a concave mirror. A `5 mm` long image of the awl pin is formed at `30 cm` in front of the mirror. The focal length of this mirror is

Options

A. `-30` cm
B. `-20` cm
C. `-40` cm
D. `-60` cm

Answer

B

Explanation

Given, object size, `h = + 10.0 mm " " ( :' 1cm=10mm)`
` = +1.0 cm`
Image size, h'=5.0 mm = 0.5 cm
Image distance v = -30 cm
Focal length, f = ?
As, magnification, `m = (h'("image size"))/(h("object size"))`
Also, magnification, `m=(-v)/(u)implies(h')/(h)=(-v)/(u)`
`(0.5)/(1)=(-30)/(u)impliesu= -60 cm`
Using mirror formula, `(1)/(f)=(1)/(v)+(1)/(u)`
`implies (1)/(f)=(1)/(-30)-(1)/(60)=(-2-1)/(60)=(3)/(60)`
`implies f=-20cm`