Question

There is an insect inside a cabin eying towards a thick glass plate $P_1$. Insect sees the images of light source across the glass plate $P_1$ outside the cabin. The cabin is made of thick glass plates of refractive index $\mu =\frac{3}{2}$ and thickness is 3 cm. The insect is eying from the middle of the cabin as shown in the figure. ( glass plates are partially reflective and consider only paraxial rays)
At what distance ( from the eye of insect) will the eye see the first image?

• A. 5 cm
• B. 7cm
• C. 11 cm
• D. 14cm

Answer 1

The correct option is D 14cm

$\begin{array}{c}\text{The insect can see the light because of the}\\ \text{rays which refract at}{P}_2\text{and which}\\ \text{reflect at}{P}_1\\ \text{Hence we have to consider shift at}{P}_2\\ \text{and mirror at}{P}_1\end{array}$

$\begin{array}{c}\text{Shift of the light ray at}{P}_2\\ \text{Shift}=t(1-\frac{1}{\mu })\\ \text{where.}\mu =\text{refractive index of slab}\\ t=\text{thick ness of slab.}\\ \text{shift}=3(1-\frac{1}{\frac{3}{2}})\\ =1cm\\ =\text{so distance of refracted object from P\_1}\\ =3+3+3+2\end{array}$

$=11cm$

Distance of the first image seen by eye = Image distance form mirror + object distance from mirror

$\begin{array}{c}=11+3\\ =14cm\end{array}$

so option $D$ is correct.