With a concave mirrorr, an object is placed at a distance `x_(1)` from the principal focus, on the principal axis. The image is formed at a distance `x_(2)` from the principal focus. The focal length of the mirrorr is

Options

A. `x_(1)x_(2)`
B. `(x_(1)+x_(2))//2`
C. `sqrt(x_(1)//x_(2)`
D. `sqrt(x_(1)x_(2))`

Answer

d.

Explanation

`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(f-x_(1))+(1)/(f-x_(2))=(1)/(f)` or `(f-x_(2)+f-x_(1))/((f-x_(1))(f-x_(2)))=(1)/(f)`
or`f^(2)-fx_(2)-fx_(1)+x_(1)x_(2)=2f^(2)-f(x_(1)+x_(2))`
or `f^(2)=x_(1)x_(2) or f=sqrt(x_(1)x_(2))`
This is Newton's mirror formula.