Embibe Experts Solutions for Chapter: Ray Optics and Optical Instruments, Exercise 1: Exercise

Explain the formation of a mirage.

A right-angled prism is kept immersed in water. When a ray of light is allowed to be incident on one of the faces of the prism adjoining the right angle normal to the face, the ray is found to be totally reflected by the face opposite to the right angle and to emerge through the other face adjoining the right angle. But when the ray of light is allowed to be normally incident on the other face adjoining the right angle, it emerges through the face opposite to the right angle and there is total internal reflection.

If the other two angles of the prism be $60°$ and $30°$, what information can you gather about the refractive index of the material of the prism? Given RI of water with respect to vacuum$=1.33$ and $V_3=1.732.$

A small bulb is placed at the bottom of a tank containing water to a depth of $80 cm.$ What is the area of the surface of water through which light from the bulb can emerge out? The Refractive index of water is 1.33. Consider the bulb to be a point source of light.  

Light is incident at an angle $\alpha$ on one planer end of a transparent cylindrical rod of refractive index n. Determine the least value of $n$ so that the light entering the rod does not emerge from the curved surface of rod irrespective of the value of $\alpha$. 

What is meant by critical angle for a given refracting medium? Establish a relationship between critical angle and refractive index. What is a total internal reflection, and when does it take place?

The refractive index of the material of a concave lens is $\mathrm{n}$. It is immersed in a medium of refractive index $n_1$. A parallel beam of light is incident on the lens. Trace the path of the emergent rays in each of the following cases:(i) ${\mathrm{n}}_1=\mathrm{n}$ (ii)${\mathrm{n}}_1> \mathrm{n}$ and (iii)${\mathrm{n}}_1< \mathrm{n}$.

What is transverse magnification? Derive an expression, with the help of ray-diagrams, for magnification for a different types of images in convex and concave lenses.

Dose total internal reflection take places in a rainbow ?