The following figure shows the section $ABC$ of an equilateral triangular prism. A ray of light enters the prism along$\mathit{ }LM$ and emerges along $QD$. If the refractive index of the material of the prism is $1.6$, angle $LMN$ is

 

Two plane mirrors are placed as shown in the figure and a point object $O$ is placed at the origin 

(a) How many images will be formed.

(b) Find the position(s) of image(s).

(c) Will the incident ray passing through a point $P (1, 1.25)$ take part in image formation.

Two spherical mirrors (convex and concave) having the same focal length of $36 \mathrm{cm}$ are arranged as shown in the figure so that their optical axes coincide. The separation between the mirrors is $1 \mathrm{m}$. At what distance from the concave mirror should an object be placed so that its images formed by the concave and convex mirrors independently are identical in size?

A light ray falling at an angle of $45°$ with the normal on the surface of a clean slab of ice of thickness $1.00 \mathrm{m}$ is refracted into it at an angle of $30°$. Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum$=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$.

In the given figure, an observer in air $(n=1)$ sees the bottom of a beaker filled with water $(n=4/3)$ upto a height of $40 \mathrm{cm}$. What will be the depth felt by this observer.