Embibe Experts Solutions for Chapter: Ray Optics, Exercise 4: Exercise-4

One side of radius of curvature $R_1=120 \mathrm{cm}$ of a convex lens of refractive index $\mu =\frac{3}{2}$ and focal length $f_1=20 \mathrm{cm}$ is silvered. It placed on a horizontal surface with silvered surface is contact with it. Another convex lens of focal length $f_2=20 \mathrm{cm}$ is fixed coaxially $d=10 \mathrm{cm}$ above. A luminous point object $O$ on the axis gives rise to an image coincident on it . Find its height above the upper lens.

A right angle prism $\left(45°-90°-45°\right)$ of refractive index $n$ has a plane of refractive index $n_1$ $\left(n_1<n\right)$ cemented to its diagonal face. The assembly is in air. The ray is incident on $AB$.

(i) Calculate the angle of incidence at $AB$ for which the ray strikes the diagonal face at the critical angle.

(ii) Assuming $n=1.352$, calculate the angle of incidence at $AB$ for which the refracted ray passes through the diagonal face undeviated. ($\sin 73°\approx 0.96$)

A glass wedge with a small angle of refraction $\theta$ is placed at a certain distance from a converging lens with a focal length $f$, one surface of the wedge being perpendicular to the optical axis of the lens. A point sources $S$ of light is one the other side of the lens at its focus. The rays reflected from the wedge (not from base) produce, after refraction in the lens, two images of the source displaced with respect to each other by $d$. Find the refractive index of the wedge glass. [Consider only paraxial rays]. 

A log solid cylindrical glass rod of refractive index $\frac{3}{2}$ is immersed in a liquid of refractive index $\frac{3\sqrt{3}}{4}$. The ends of the rod are perpendicular to the central axis of the rod. A light enters one end of the rod at the central axis as shown in the figure. A light enters one end of the rod at the central axis as shown in the figure. Find the maximum value of angle $\theta$ for which total internal reflection occurs inside the rod?

In the figure shown $L$ is converging lens of focal length $10 \mathrm{cm}$ and $M$ is a concave mirror of radius of curvature $20 \mathrm{cm}$. A point object $O$ is placed in front of the lens at a distance $15 \mathrm{cm}$. $AB$ and $CD$ are optical axes of the lens and mirror respectively. Find the coordinates of the final image formed by this system taking $O$ as origin. The distance between $CD$ & $AB$ is $1 \mathrm{mm}$.

An equilateral prism deviates ray through $23°$ for two angles of incidence differing by $23°$. Find $\mu$ of the prism.

The figure shows the path of a ray passing through an equiangular prism $PQR$. It is incident on face $PR$ at an angle slightly greater than the critical angle for total internal reflection. If the angle $\alpha$ shown in the figure is $30°$. Calculate the Refractive index of the material of the prism.

In the figure shown $S$ is a monochromatic point source emitting light of wavelength $=500 \mathrm{nm}$. A thin lens of circular shape and focal length $0.10 \mathrm{m}$ is cut into two identical halves $L_1$ and $L_2$ by a plane passing through a diameter. The two halves are placed symmetrically about the central axis SO with a gap of $0.5 \mathrm{mm}$. The distance along the axis from $S$ to $L_1$ and $L_2$is $0.15 \mathrm{m}$, while that from $L_1$ and $L_2$ to $O$ is $1.30 \mathrm{m}$.

The screen at $O$ is normal to SO. (i) If the third intensity maximum occurs at the point $A$ on the screen, find the distance OA. (ii) If the gap between $L_1$ and $L_2$ is reduced from its original value of $0.5 \mathrm{mm}$, will the distance OA increase decrease or remain the same?