Q138 / 180 · AIIMS 2009 · Physics

In a concave mirror, an object is placed at a distance $d_1$ from the focus and the image is formed at a distance $d_2$ from the focus. Then the focal length of the mirror is

  • Correct answer
    A
    $\sqrt{d_1 d_2}$
  • B
    $d_1 d_2$
  • C
    $\left(d_1+d_2\right) / 2$
  • D
    $\sqrt{d_1 / d_2}$

Solution

$\mathrm{U} \operatorname{sing} \frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ Given $u=f+d_1 \quad v=f+d_2$ $f=\frac{u v}{u+v}=\frac{\left(f+d_1\right)\left(f+d_2\right)}{\left(f+d_1\right)+\left(f+d_2\right)}$ On solving $f=\sqrt{d_1 d_2}$

Hence, the correct answer is option: 'A'.

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