Question

In a concave mirror, an object is placed at a distance x₁ from focus, and image is formed at a distance x₂ from focus. Then focal length of mirror is(a) $\sqrt{x_{1}x_{2}}$(b) $\frac{x_{1}-x_{2}}{2}$(c) $\frac{x_{1}+x_{2}}{2}$(d) $\sqrt{\frac{x_{1}}{x_{2}}}$

Answer 1

Given,
Object distance, u=-(x1 +f)
Image distance, v= -(x2 +f)
Focal length,F=-f
Using mirror formula,
1/v + 1/u=1/F
-1/(x2 +f) - 1/ (x1 +f)=-1/f
On solving, we get
f=√x1x2