Embibe Experts Solutions for Chapter: Geometrical Optics, Exercise 2: Exercise#2

A girl sees through a circular glass slab(refractive index $1.50$ of thickness $20 \mathrm{mm}$ and diameter $60 \mathrm{cm}$ to the bottom of a swimming pool. Refractive index of water is $1.33$. The bottom surface of the slab is in contact with the water surface.

The depth of the swimming pool is $6 \mathrm{m}$. The area of bottom of swimming pool that can be seen through the slab is approximately

A point object is placed $20 \mathrm{cm}$ left of a convex lens of focal length $f=5 \mathrm{cm}$ (see the figure). The lens is made to oscillate with small amplitude $A$ along the horizontal axis. The image of the object will also oscillate along the axis with

A cubical vessel has opaque walls. An observer (dark circle in figure below) is located such that she can see only the wall $CD$ but not the bottom. Nearly to what height should water be poured so that she can see an object placed at the bottom at a distance of $10 \mathrm{cm}$ from the corner $C$? (Refractive index of water is $1.33$.)

Electromagnetic waves emanating from a point $A$ (in the air) are incident on a rectangular block of material $M$ and emerge from the other side as shown. The angles $i$ and $r$ are angles of incidence and refraction when the wave travels from air to the medium. Such paths for the rays are possible

A glass prism has a right-triangular cross section $ABC$, with $\angle A=90°$. A ray of light parallel to the hypotenuse $BC$ and incident on the side $AB$ emerges grazing the side $AC$. Another ray, again parallel to the hypotenuse $BC$, incident on the side $AC$ suffers total internal reflection at the side $AB$. Which one of the following must be true about the refractive index $\mu$ of the material of the prism?

It was found that the refractive index of material of a certain prism varied as $1.5+\frac{0.004}{{\lambda }^2},$ where $\lambda$ is the wavelength of light used to measure the refractive index. The same material was then used to construct a thin prism of apex angle $10°$. Angles of minimum deviation $\left({\delta }_{\mathrm{m}}\right)$ of the prism were recorded for the sources with wavelengths ${\lambda }_1$ and ${\lambda }_2$ respectively. Then

A parallel beam of light is incident on a tank filled with water up to a height of $61.5 \mathrm{mm}$ as shown in the figure below. Ultrasonic waves of frequency $0.5 \mathrm{MHz}$ are sent along the length of the water column using a transducer placed at the top, and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen? Take the speed of sound in water to be $1,500 \mathrm{m} {\mathrm{s}}^{-1}$.

Consider a glass cube slab of dielectric bound by the planes, $x=0\text{,} x=a\text{;} y=0\text{,} y=b\text{;} z=0\text{,} z=c$ with $b>a>c$. The slab is placed in air and has a refractive index of $n$. The minimum value of $n$ such that all rays entering the dielectric at $y=0$ reach $y=b$ is,