The angle of a prism is $30^o$ and its refractive index is $\sqrt{2}$. One of its surfaces is silvered. At what angle of incidence should a ray be incident on the other surface so that after reflection from the silvered surface,it retraces its path?

$A$ ray falls on a prism $ABC$ $(AB = BC)$ and travels as shown in the figure. The minimum refractive index of the prism material should be

$A$ ray of light is incident on the first face of an equilateral glass prism at an angle of incidence '$i$'. The emergent ray just grazes along the adjacent face. The refractive index of the prism is $\sqrt{2}$. The value of the angle of incidence at the first face is $(\sin 45^{\circ} = 1/\sqrt{2}, \sin 90^{\circ} = 1)$.

$A$ prism of refractive index $\mu$ and angle of prism $A$ is placed in the position of minimum angle of deviation. If the minimum angle of deviation is also $A$, then the value of $A$ in terms of refractive index $\mu$ is ..... .

Three prisms of crown glass,each having a prism angle of $9^o$,and two prisms of flint glass are used to make a direct vision spectroscope. What will be the angle of the flint glass prisms in degrees if the refractive index $\mu$ for flint glass is $1.60$ and $\mu$ for crown glass is $1.53$ (in $^o$)?

$A$ thin prism of angle $5^{\circ}$ is placed at a distance of $10\,cm$ from an object. What is the distance of the image from the object? (Given refractive index $\mu$ of prism $= 1.5$)