Calculate the critical angle for a glass-air surface,if a ray of light incident in air on the glass surface is deviated by $15^{\circ}$ when the angle of incidence is $45^{\circ}$. (in $^{\circ}$)

$A$ material is embedded between two glass plates. The refractive index $n$ of the material varies with thickness as shown in the figure. The maximum incident angle (in degrees) on the material for which the beam will pass through the material is

$A$ parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius $R=0.05 \ m$ and refractive index $n=1.5$, placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose nearest distance $x$ from the cylinder is

$A$ ray of light in a liquid of refractive index $1.4$ approaches the boundary surface between the liquid and air at an angle of incidence whose sine is $0.8$. Which of the following statements is correct about the behavior of the light?

What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding respectively?

For total internal reflection to take place,the angle of incidence $i$ and the refractive index $\mu$ of the medium must satisfy the inequality