An infinitely long rod lies along the axis of a concave mirror of focal length $f$. The near end of the rod is at a distance $u>f$ from the mirror. Its image will have a length

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: