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

A parallel beam of light is incident on a transparent sphere of refractive index '$n$'. If the beam finally gets focussed at a point situated at a distance $=2\times$(radius of sphere) from the centre of the sphere, then find $n$.

A thin equiconvex lens of glass of refractive index $\mu =\frac{3}{2}$ and of focal length $0.3 \mathrm{m}$ in air is sealed into an opening at one end of a tank filled with water $\mu =\frac{4}{3}$. On the opposite side of the lens, a mirror is placed inside the tank on the tank wall perpendicular to the lens axis, as shown in figure. The separation between the lens and the mirror is $0.8 \mathrm{m}$ A small object is placed outside the tank in from of the lens at a distance of $0.9 \mathrm{m}$ from the lens on its axis. Find the position (distance in $\mathrm{cm}$) of the image of the object formed by the systme from the lens).

An object is kept at a distance of $16 \mathrm{cm}$ from a thin lens and the image formed is real. If the object is kept at a distance of $6 \mathrm{cm}$ from the same lens the image formed is virtual. If the size of the image formed are equal, then find the focal length (in $\mathrm{cm}$) of the lens?

A point source of light is kept at a distance of, $15 \mathrm{cm}$ from a converging lens, on its optical axis. The focal length of the lens is, $10 \mathrm{cm}$ and its diameter is, $3 \mathrm{cm}$. A screen is placed on the other side of the lens, perpendicular to the axis of lens, at a distance, $20 \mathrm{cm}$ from it. If the area of the illuminated part of the screen is $\frac{\pi }{k} {\mathrm{cm}}^2$, then find $k$.

A lens placed between a candle and a screen forms a real triply magnified image of the candle on the screen. When the lens is moved away from the candle by $0.8 \mathrm{m}$ without changing the position of the candle, a real image one-third the size of the candle is formed on the screen. Determine the focal length (in $\mathrm{cm}$) of the lens.

Consider a 'beam expander' which consists of two converging lenses of focal lengths $40 \mathrm{cm}$ and $100 \mathrm{cm}$ having a common optical axis. A laser beam of diameter $4 \mathrm{mm}$ is incident on the $40 \mathrm{cm}$ focal lens. Then what is the diameter (in $\mathrm{cm}$) of the final beam (see figure)?

A prism of refractive index $\sqrt{2}$ has refracting angle $60°$. Find the angle of incidence (in degree) so that a ray suffers minimum deviation.

In the given figure the angle (in degree) between the velocity of object and image is $\alpha$. The value of $\frac{\alpha }{10}$ is