$A$ thin prism of angle $6^{\circ}$ made of glass of refractive index $1.5$ is combined with another prism made of glass of refractive index $1.75$ to produce dispersion without deviation. Then the angle of the second prism is ...... (in $^{\circ}$)

If $r$ and $r^1$ denote the angles of refraction at the two faces of a prism with a prism angle of $50^{\circ}$,and $r$ varies with time $t$ as $r = 10^{\circ} + t^2$,how will $r^1$ vary with time?

$A$ prism of refractive index $n_{1}$ and another prism of refractive index $n_{2}$ are stuck together (as shown in the figure). $n_{1}$ and $n_{2}$ depend on $\lambda$, the wavelength of light, according to the relation:
${n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text{ and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}$
The wavelength for which rays incident at any angle on the interface $BC$ pass through without bending at that interface will be $....\,nm.$

Define the angle of minimum deviation.

For an equilateral prism,it is observed that when a ray strikes grazingly at one face,it emerges grazingly at the other. Its refractive index will be

$A$ ray of light suffers a minimum deviation when incident on an equilateral prism of refractive index $ \sqrt{2} $. The angle of incidence is (in $^{\circ}$)