Embibe Experts Solutions for Chapter: Ray Optics, Exercise 3: Exercise - 3

A ray of light travelling in water is incident on its surface open to air. The angle of incidence is $\theta$, which is less than the critical angle. Then, there will be

Statement $1$. The formula connecting $u, v,\text{ and} f$ for a spherical mirror is valid only for mirrors whose size is very small compared to their radii of curvature. Statement $2$. Laws of reflection are strictly valid for a plane surface, but not for a large spherical surface.

A ball is dropped from a height of $20 \mathrm{m}$ above the surface of water in a lake. The refractive index of water is $\frac{4}{3}.$ A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8 \mathrm{m}$ above the water surface, the fish sees the speed of the ball as (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The focal length of a thin biconvex lens is $20 \mathrm{cm}$. When an object is moved from a distance of $25 \mathrm{cm}$ in front of it to $50 \mathrm{cm}$, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is,

A biconvex lens of focal length $15 \mathrm{cm}$ is in front of a plane mirror. The distance between the lens and the mirror is $10 \mathrm{cm}$. A small object is kept at a distance of $30 \mathrm{cm}$ from the lens. The final image is 

Image of an object, approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} \mathrm{m}$ to $\frac{50}{7} \mathrm{m}$ in $30 \mathrm{s}.$ What is the speed of the object in ${\mathrm{kmh}}^{-1}.$

A large glass slab $\left(\mu =\frac{5}{3}\right)$ of thickness $8 \mathrm{cm}$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \mathrm{cm}$. What is the value of $R$?

A beaker contains water upto a height $h_1$ and kerosene of height $h_2$ above water so that the total height of the (water + kerosene) is $h_1+h_2$. Refractive index of water is ${\mu }_1$ and that of kerosene is ${\mu }_2$. The apparent shift in the position of the bottom of the beaker when viewed from above is