All lights are switched off, except for a bright point-light source kept at the bottom of a swimming pool filled with clear water of refractive index $4/3 .$As a result, only a circular patch of $6 \mathrm{m}$ diameter of the water surface is visible to spectators standing around the swimming pool. Which of the following gives the nearest value of the depth of the pool?

Three rays of light, namely red $\left(R\right)$, green $\left(G\right)$ and blue $\left(B\right)$ are incident on the face $PQ$ of a right angled prism $PQR$ as shown in figure.

The refractive indices of the material of the prism for red, green and blue wavelength are $1.27,1.42$ and $1.49$ respectively. The colour of the ray(s) emerging out of the face $PR$ is :

A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i.$ The reflected and refracted rays make an angle of $90°$ with each other. The angle of reflection and refraction are respectively $r$ and $r^{\text{'}}.$ The critical angle is given by,

A ray of light originates from inside a glass slab and is incident on its inner surface at an angle $\mathrm{\theta }$ as shown,

In this experiment the location $x$ of the spot where they ray hits the screen is recorded. Which of the following correctly shown the plot of variation of $x$ with the angle $\mathrm{\theta }$ ?

White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains

In the given figure, if object is placed at a distance of $9 \mathrm{cm}$ from $O_1$, then find the image distance $\left(\mathrm{in} \mathrm{cm} \right)$ from $O_2$•