A short linear object of length $b$ lies along the axis of a concave mirror of focal length $f,$at a distance $u$ from the mirror. The size of the image is approximately

What is the length of the image of the rod in mirror, according to the observer in air? (refractive index of the liquid is $\mathrm{\mu }$)

Two thin slabs of refractive indices ${\mathrm{\mu }}_1$ and ${\mathrm{\mu }}_2$ are placed parallel to each other in the $\mathrm{x}-\mathrm{y}$ plane. If the direction of propagation of a ray the two media are along the unit vectors ${\hat{\mathrm{r}}}_1=\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}$ and ${\hat{\mathrm{r}}}_2=\mathrm{c}\hat{\mathrm{i}}+\mathrm{d}\hat{\mathrm{j}}$ then we have 

A point source $\mathrm{S}$ is placed at the bottom of different layers as shown in the figure. The refractive index of bottommost layer is ${\mathrm{\mu }}_0$. The refractive index of any other upper layer is $\mathrm{\mu }\left(\mathrm{n}\right)={\mathrm{\mu }}_0+\frac{{\mathrm{\mu }}_0}{4\mathrm{n}-18}$ A ray of light with angle $\mathrm{i}=30°$ start from the source $\mathrm{S}$. Total internal reflection takes place at the upper surface of layer having $\mathrm{n}$ equal to

A ray light strikes a cubical slab surrounded by air as shown in the figure. Then the geometrical path length traversed by the light in the slab will be:

A cubical block of glass of refractive index ${\mathrm{n}}_1$ is in contact with the surface of water of refractive index ${\mathrm{n}}_2$. A beam of light is incident on vertical face of the block (see figure). After refraction, a total internal reflection at the base and refraction at the opposite vertical face, the ray emerges out at an angle $\mathrm{\theta }$. The value of $\mathrm{\theta }$ is given by-

A beam of diameter $\text{'}\mathrm{d}\text{'}$ is incident on a lass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to $\mathrm{d}$, then the diameter of the beam at the base the hemisphere will be: