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

A beam of light passing from air into a transparent medium, suffers a deviation of $15°$ at the interface, when incident at an angle of $60°$. The speed of light in the medium is

A point source $O$ is placed at a distance of $12.5 \mathrm{cm}$ from a converging lens of focal length $10 \mathrm{cm}$, on its principal axis as shown in the figure. Find the distance at which a diverging mirror of focal length $20 \mathrm{cm}$ should be placed, so that a real image is formed on the source itself.

A screen is placed at a distance of $90 \mathrm{cm}$ from an object. A convex lens forms the image of this object on the screen, when placed at two different locations separated by $30 \mathrm{cm}$ as shown in the figure. Determine the focal length of the lens.

With the help of a neat ray diagram, derive the relationship between the focal length, the object distance and the image distance for a concave mirror. A concave mirror is first kept in a medium of refractive index $1.33$ and then in another medium of refractive index $1.4$. What will be the change in its focal length?

A spherical surface of radius of curvature  separates a rarer and a denser medium. With the help of a neat ray diagram obtain the relationship between the object distance $‘u’$, the image distance $‘v’$, the radius of curvature $‘R’$ and the refractive indices $n_1$ and $n_2$ of the two media, when the object is kept in the rarer medium.

How does the scattering of light vary with the wavelength of different colours of light ?

The radius of curvature of either face of a convex lens is equal to its focal length. Calculate the refractive index of the material of the lens.

With the help of a diagram, obtain an expression for the refractive index of the material of the prism. If $\theta$  is the angle of incidence and the refracted ray inside the prism is parallel to the base, then what will be the angle of emergence ?

With the help of a diagram, obtain a relation between object distance, image distance and focal length of a concave mirror. If the concave mirror is immersed in water, will the above equation be still valid ?