A light ray is incident on a transparent sphere of index$=\sqrt{2}$. at a angle of incidence$=45°$. What is the deviation of a tiny fraction of the ray, which enters the sphere, undergoes two internal reflections and then refracts out into air?

A paraxial beam is incident on a glass $\left(\mathrm{n}=1.5\right)$ hemisphere of radius $\mathrm{R}=6\mathrm{cm}$ in air as shown. The distance of point of convergence $\mathrm{F}$ form the plane surface of hemisphere  is:

A concave spherical surface of radius of curvature $10\mathrm{cm}$, separates two medium $\mathrm{X}$ and $\mathrm{Y}$ of $\mathrm{R}.\mathrm{I}. 4/3$ and $3/2$ respectively. If the object placed along principal axis in medium $\mathrm{X}$, then:

A double convex lens, made of a material of refractive index ${\mathrm{\mu }}_1$, is placed inside two liquids of refractive indices ${\mathrm{\mu }}_2$ and ${\mathrm{\mu }}_3$, as shown. ${\mathrm{\mu }}_2>{\mathrm{\mu }}_1>{\mathrm{\mu }}_3$. A wide, parallel beam of light is incident on the lens from the left. The lens will given rise to:

A converging lens of focal length $20\mathrm{cm}$ and diameter $5\mathrm{cm}$ is cut along the line $\mathrm{AB}$. The part of the lens shown shaded in the diagram is now used to from an image of a point $\mathrm{P}$ placed $30\mathrm{cm}$ away from it on the line $\mathrm{XY}$ which is perpendicular to plane of the lens. The image of $\mathrm{P}$ will be formed.

Look at the ray diagram shown, what will be the focal length of the $1^{\mathrm{st}}$ and the $2^{\mathrm{nd}}$ lens, If the incident light ray passes without any deviation?

A diverging lens of focal length $10\mathrm{cm}$ is placed $10\mathrm{cm}$ in front og a plane mirror as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance: