An object is 30.0 cm from a spherical mirror along the central axis. The absolute value of lateral magnification is `(1)/(2)`. The image produced is inverted. What is the focal length of the mirror?

Options

A. 10 cm
B. `-10 cm`
C. `- 15`
D. 15

Answer

B

Explanation

Image is inverted so it is real, u and v both are negative. Magnification is `(1)/(2)`, therefore, `v=(u)/(2)`.
Given, u = - 30 cm and v = - 15 cm
Using the mirror formula,
`(1)/(v)+(1)/(u)=(1)/(f)`
we have, `(1)/(f)=(1)/(-15)-(1)/(30)=-(1)/(10)`
`therefore` Focal length `f= -10 cm`