Reflection of Light — Question 7

Given,

u = 40 cm (negative)

f = 40 cm (positive)

Mirror formula:

$\dfrac{1}{\text u} + \dfrac{1}{\text v} = \dfrac{1}{\text f}$

Substituting the values in the formula above, we get,

$- \dfrac{1}{40} + \dfrac{1}{\text v} = \dfrac{1}{40} \\[0.5em] \dfrac{1}{\text v} = \dfrac{1}{40} + \dfrac{1}{40} \\[0.5em] \dfrac{1}{\text v} = \dfrac{1+1}{40} \\[0.5em] \dfrac{1}{\text v} = \dfrac{2}{40} \\[0.5em] \dfrac{1}{\text v} = \dfrac{1}{20} \\[0.5em] \Rightarrow \text v = 20 \text{ cm} \\[0.5em]$

Hence, the image is formed 20 cm behind the mirror.