For concave mirror, image obtained at `d_2` from focus for object at `d_1` from focus . The focal length of mirror will be ......

Options

A. `f=sqrt(d_1d_2)`
B. `d_1d_2`
C. `((d_1+d_2))/(2)`
D. `sqrt(d_1/d_2)`

Answer

A, B, D

Explanation

In `1/v+1/u=1/f,u=f+d_1` by taking `v=f+d_2`
`f=(uv)/(u+v)`
`f=((f+d_1)(f+d_2))/(f+d_1+f+d_2)`
`therefore f^2+fd_1+f^2+fd_2=f^2+fd_2+fd_1+d_1d_2`
`therefore f^2=d_1d_2`
`therefore f=sqrt(d_1d_2)`