The figure shows the square front face (of side $a$) of a transparent cuboidal block. The thickness or the third dimension of the block is negligible in comparison to $a$. The block has uniform refractive index $\mathrm{\mu }$ equal to $2$. A point source $S$ which can emit light in all directions can move inside the block. It is desired that no light of $S$ should pass through $AB$. Sketch the region in which $\mathrm{S}$ should be present to satisfy this condition.

 

An insect at point $P$ sees its two images in the water-mirror system as shown in the figure. One image is formed due to direct reflection from the water surface and the other image is formed due to refraction, reflection and again refraction by the water mirror system in order. Find the separation between the two images. Mirror has a focal length $60 \mathrm{cm}. (n_{\mathrm{w}}=4/3)$

In the given figure, if observer sees the bottom of vessel at $8 \mathrm{cm}$, find the refractive index of the medium in which observer is present.

A man starting from point $P$ crosses a $4 \mathrm{km}$ wide lagoon and reaches point $Q$ in the shortest possible time by the path shown in the figure. If the person swims at a speed of $3 \mathrm{km} {\mathrm{h}}^{-1}$ and walks at a speed of $4 \mathrm{km} {\mathrm{h}}^{-1}$, then his time in minutes of journey is $\left({\mu }_{\mathrm{salt}water}=\frac{4}{3}\right)$:

In the given figure, the faces of the prism $ABCD$ made of glass with a refractive index $n$ form dihedral angles $\angle A=90°, \angle \mathrm{B}=75°, \angle \mathrm{C}=135° \& \angle \mathrm{D}=60°$ (The Abbe's prism ). A beam of light falls on the face $\mathrm{AB}$ & after total internal reflection from face, $BC$ escapes through face $AD$. Find the range of $n$ and angle of incidence $\mathrm{\alpha }$ of the beam onto face $AB$, if a beam that has passed through the prism in this manner is perpendicular to the incident beam.

A point source of light is placed at a distance h below the surface of a large deep lake. (a) Show that the fraction $f$ of the light energy that escapes directly from the water surface is independent of h and is given by $f=\frac{1}{2}-\frac{1}{2n}\sqrt{n^2-1}$, where $n$ is the index of refraction of water.

(Note: Absorption within the water and reflection at the surface except where it is total, have been neglected)

(b) Evaluate this ratio for $n=\frac{4}{3}$.

A glass prism with a refracting angle of $60°$ has a refractive index $1.52$for red and $1.6$ for violet light. A parallel beam of white light is incident on one face at an angle of incidence which gives minimum deviation for red light. Find:

(a) the angle of incidence

(b) angular width of the spectrum

(c) the length of the spectrum if it is focussed on a screen by lens of focal length $100 \mathrm{cm}$.

In the given figure, $O$ is a point object kept on the principal axis of a concave mirror $M$ of radius of curvature $20 \mathrm{cm}$. $P$ is a prism of angle $\alpha =1.8°$. Light falling on the prism (at a small angle of incidence) gets refracted through the prism and then falls on the mirror. The refractive index of the prism is $3/2$. Find the distance between the images formed by the concave mirror due to this light.