Question

As shown in the figure, an object O is at the position ($-10,2$) with respect to the origin P. The concave mirror $M_1$ has radius of curvature $30\text{cm}$. A plane mirror $M_2$ is kept at a distance of $40\text{cm}$ in front of the concave mirror. Consider first reflection on the concave mirror $M_1$ and second on the plane mirror $M_2$. Find the coordinates of the second image w.r.t the origin P.

• A. $(45,70)$
• B. $(-45,70)$
• C. $(-46,-70)$
• D. $(-46,70)$

Answer 1

The correct option is C $(-46,-70)$


For $M_1,u=-10\text{cm},f=-15\text{cm},h=2\text{cm}$

Using mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}+\frac{1}{-10}=\frac{1}{-15}$
$\Rightarrow \frac{1}{v}=\frac{1}{10}-\frac{1}{15}=\frac{3-2}{30}$
$\Rightarrow v=30\text{cm}$

and $\frac{h_2}{h_1}=-\frac{v}{u}\Rightarrow h_2=6\text{cm}$

The image formed by the plane mirror is $70\text{cm}$ below the principal axis and $70+6-30=46\text{cm}$ to the left of the mirror.
Therefore, coordinates of $I_2$ w.r.t P are (-46, -70).