Question

What is the formula for spherical mirrors for object distance p and image distance q ?

• A. $\frac{1}{p}+q=\frac{1}{f}$
• B. $\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$
• C. $\frac{1}{p}+\frac{1}{q}=f$
• D. $p+\frac{1}{q}=\frac{1}{f}$

Answer 1

The correct option is B $\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$

Mirror formula is given as:

$\frac{2}{R}=\frac{1}{v}+\frac{1}{u}$
where, $R$ is the radius of curvature of the spherical mirror
$u$ is the object distance from the pole
$v$ is the image distance from the pole

We know,
$f=\frac{R}{2}$
$\Rightarrow \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\therefore$ For object distance $p$ and image distance $q$, mirror formula becomes

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$
Hence, the correct answer is OPTION B.