Question

A mirror of radius of curvature $20\text{cm}$ and an object which is placed at a distance of $15\text{cm}$ are both moving with the velocities $1\text{m/s}$ and $10\text{m/s}$ as shown in the figure. The velocity of the image is

• A. $20{\text{ms}}^{-1}$
• B. $30{\text{ms}}^{-1}$
• C. $45{\text{ms}}^{-1}$
• D. $90{\text{ms}}^{-1}$

Answer 1

The correct option is C $45{\text{ms}}^{-1}$

Given that,
radius of curvature $R=-20\text{cm}$ and
object distance $u=-15\text{cm}$

Using mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{2}{R}$,

we get
$\frac{1}{v}-\frac{1}{15}=-\frac{1}{10}\Rightarrow v=-30\text{cm}$

Now, using
$V_{im}=-\frac{v^2}{u^2}{V}_{om}$
$(V_i-V_m)=-\frac{v^2}{u^2}(V_o-V_m)$
$\Rightarrow V_i-\left(1\right)=-\frac{(-30{)}^2}{(-15{)}^2}\left[\right(-10)-(1\left)\right]$
$\Rightarrow V_i=45\text{m/s}$
So, the image will move with velocity of $45\text{m/s}$

Why this Question? Concept: Remember that the mirror equation holds for spherical mirrors only at small distances, at larger distances only parabolic mirrors hold this equation.