Embibe Experts Solutions for Chapter: Ray Optics and Optical Instruments, Exercise 1: Uttarakhand Board-2018

Obtain the formula for combined focal length of two thin lenses in contact.

What do you understand by resolving power of a microscope? How will resolving power of microscope be affected when Wavelength of light used decreases

What do you understand by resolving power of a microscope? How will resolving power of microscope be affected when-

$\left(\mathrm{ii}\right)$ Diameter of objective lens decreases

What do you understand by total internal reflection? Write essential conditions for it.

A tank is filled with water to a height of $12.5 \mathrm{cm}$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \mathrm{cm}$. What is the refractive index of water?

The radii of curvature of a double convex lens are $20 \mathrm{cm}$ each and refractive index of the material of the lens is $1.5$. What will be focal length of the lens?

Generally Mirage is observed in deserts. Give reason for this.

Draw the graph between angle of incidence $\left(\mathrm{i}\right)$ and angle of deviation $\left(\mathrm{\delta }\right)$ for a triangular prism and show the angle of minimum deviation in it. Prove that in the condition of minimum deviation, the refractive index $\left(\mathrm{n}\right)$ of the material of triangular prism is given by following formula-

$\mathrm{n}=\frac{\sin \left({\displaystyle \frac{\mathrm{A}+{\mathrm{\delta }}_{\mathrm{m}}}{2}}\right)}{\sin \left({\displaystyle \frac{\mathrm{A}}{2}}\right)}$

Where $\mathrm{A}$ is prism angle and ${\mathrm{\delta }}_{\mathrm{m}}$ is the angle of minimum deviation.