Question

A point object $O$ is placed in front of a concave mirror of focal length $10cm$. A glass slab of refractive index $\mu =3/2$ and thickness $6cm$ is inserted between the object and mirror.
Find the position and nature of the final image when the distance $x$ shown in figure, is $5cm$.

• A. $11cm$, virtual
• B. $17cm$, real
• C. $14cm$, real
• D. $20cm$, virtual

Answer 1

The correct option is B $17cm$, real

the shift observed due to glass slab is $t(1-\frac{1}{\mu })=6(1-\frac{2}{3})=2$

hence the object distance for mirror is $32-2=20$

$u=-30$ ;$f=-10$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{-1}{30}=\frac{-1}{10}$

$v=-15$

and the shift due to slab counts again i.e, final image distance is $15+2=17$

image is real (-ve sign)

option $B$ is correct