Question

Find the position of the image formed after the first reflection from the concave mirror as shown in the figure.

• A. at $20\text{cm}$ from mirror on the left side
• B. at $40\text{cm}$ from mirror on the left side
• C. at infinity
• D. at $10\text{cm}$ from mirror on the left side

Answer 1

The correct option is C at infinity

Given the refractive index of medium on the two sides of spherical surface,

${\mu }_1=1$

${\mu }_2=1.5$

For the first image formed due to refraction at spherical surface,

$u=-20\text{cm}$

$R=+6\text{cm}$

Using the relation between object and image distance for refraction at curved surfaces:

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

$\text{Or,}\frac{1.5}{v}-\frac{1}{(-20)}=\frac{1.5-1}{+6}$

$\text{Or,}\frac{1.5}{v}=\frac{1}{12}-\frac{1}{20}$

$\Rightarrow$ $v=\left(\frac{12\times 20}{20-12}\right)\times 1.5$

$\therefore v=\frac{240}{8}\times 1.5=45\text{cm}$


The image formed after first refraction will act as an object for the concave mirror.

From the above diagram, the object distance will be $-ve$ for concave mirror as per the sign convention.

Also the object is placed at a distance,

$PI=65-45=20\text{cm}$

$\Rightarrow u^{\prime }=-20\text{cm}$

$f=\frac{-R}{2}=\frac{-40}{2}=-20\text{cm}$

We can infer that the object is placed at the focus of concave mirror, hence its image will be formed at infinity after reflection from mirror.

Thus image distance is $\infty$

Why this question? $\underset{–}{\text{Tip}}$: Always rembember that image formed during first refraction/reflection will serve as an object for the second consecutive refraction/reflection.