Question

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?

Answer 1

Image is inverted, so it is real, u and v both are negative.
Magnification is `(1)/(2)`,therefore,v=`(u)/(2)`.
Given, u=-30cm 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