Question

In a concave mirror experiment, an object is placed at a distance $x _ { 2 }$ from the focus. The focal length of the mirror would be

• A. $x _ { 1 } x _ { 2 }$
• B. $\sqrt { x _ { 1 } x _ { 2 } }$
• C. $\frac { x _ { 1 } + x _ { 2 } } { 2 }$
• D. $\sqrt { \frac { x _ { 1 } } { x _ { 2 } } }$

Answer 1

Answer: (B)

$\sqrt { x _ { 1 } x _ { 2 } }$

Answer 2

Given $v = \left( f + x _ { 2 } \right)$

The focal length $f = \frac { u v } { u + v } = \frac { \left( f + x _ { 1 } \right) \left( f + x _ { 2 } \right) } { \left( f + x _ { 1 } \right) + \left( f + x _ { 2 } \right) }$

On solving, we get $f ^ { 2 } = x _ { 1 } x _ { 2 }$ or $f = \sqrt { x _ { 1 } x _ { 2 } }$