A spherical mirror gives real image 3 times greater than object. If distance between object and image is 100 cm, then its focal length is

Options

A. 15 cm
B. 25 cm
C. 37.5 cm
D. `-37.5 cm`

Answer

C, D

Explanation

`m=v/u`
`therefore 3=v/u`
`therefore 3=v/u`
`therefore v=3u`
Now u+v=100
`therefore u+3u=100`
`therefore 4u=100`
`therefore u=25 cm`
`therefore` Now m=`(f)/(f-u)`
`3=(f)/(f-(-25))`
`therefore3 =(f)/(f+25)`
therefore 35 -75 =f`
`therefore 2f =-75`
`therefore f=-37.5` cm