Question

Find the distance $d$ between the curved surface & the concave mirror, so that image of same size will be formed by the concave mirror after refraction from the curved surface. The object is placed at a distance of $40\text{cm}$ from the curved surface.

• A. $60\text{cm}$
• B. $70\text{cm}$
• C. $80\text{cm}$
• D. $100\text{cm}$

Answer 1

The correct option is C $80\text{cm}$

For curved surface:

${\mu }_1=1;{\mu }_2=1.5$

$u=-40\text{cm};R=10\text{cm}$

Using formula

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\Rightarrow \frac{1.5}{v}-\frac{1}{-40}=\frac{1.5-1}{10}$

$\Rightarrow \frac{1.5}{v}+\frac{1}{40}=\frac{1}{20}$

$\therefore v=60\text{cm}$

For concave mirror:

For the same size of the image as that of object need to be placed at the center of curvature of concave mirror.

Therefore, sum of image distance $v$ and radius of curvature $R$ of the concave mirror must be equal to $d$.

$\therefore d=v+R$

$d=60+20=80\text{cm}$

Hence, option $\left(c\right)$ is correct.