In the figure, a light ray in water is incident at angle ${\mathrm{\theta }}_1$ on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction ${\mathrm{\theta }}_2$ versus the incident angle ${\mathrm{\theta }}_1$ is given in the figure $b$. The vertical axis scale is set by ${\mathrm{\theta }}_{2\mathrm{s}}=80°$. Without calculation, determine whether the index of refraction of $\left(a\right)$ material $1$ and $\left(b\right)$ material $2$ is greater or less than the index of water $(n=1.33) .$ What is the index of refraction of $\left(c\right)$ material $1$ and $\left(d\right)$ material $2$?

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

The figure shows a small light bulb suspended at distance $d_1=300 \mathrm{cm}$ above the surface of the water in a swimming pool, where the water depth is $d_2=200 \mathrm{cm}.$ The bottom of the pool is a large mirror. How far below the mirror surface is the image of the bulb? (Hint: Assume that the rays are close to a vertical axis through the bulb, and use the small-angle approximation in which $\mathrm{sin\theta }=\mathrm{tan\theta }\approx \mathrm{\theta }$).

A container contains water up to a height of $20 \mathrm{cm}$ and there is a point source at the centre of the bottom of the container. A rubber ring of radius $r$ floats centrally on the water. The ceiling of the room is $2.0 \mathrm{m}$ above the water surface.

(a) Find the radius of the shadow of the radius of the ring formed on the ceiling if $r=15 \mathrm{cm}$.

(b) Find the maximum value of $r$ for which the shadow of the ring is formed on the ceiling. Refractive index of water$=\frac{4}{3}$.

It is possible to observe total internal reflection when light travels from: