Parallel rays of light are falling on convex spherical surface of radius of curvature $R=20$ cm as shown. Refractive index of the medium is $\mathrm{\mu }=1.5$. After refraction from the spherical surface parallel rays

For refraction at a convex spherical surface of radius of curvature$\mathrm{R}$ from a medium of refractive index ${\mathrm{n}}_1$ to medium of refractive index ${\mathrm{n}}_2({\mathrm{n}}_2>{\mathrm{n}}_1)$, establish the relation:

$\frac{\mathrm{n}}{\mathrm{v}}-\frac{\mathrm{n}}{\mathrm{u}}=\frac{{\mathrm{n}}_2-{\mathrm{n}}_1}{\mathrm{R}}$.

 What will be behaver of a convex lens of the refractive index $1.47$ when it is immersed in a liquid of refractive index $1.47$?

A light ray enters a solid glass sphere of refractive index $\mathrm{\mu }=\sqrt{3}$ at an angle of incidence $60°$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is:

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)

A magician during a show makes a glass lens with $\mathrm{n} =1.47$ disappear in a trough of liquid.

Could the liquid be water?

Derive an expression for refraction at a single(convex) spherical surface, i.e. a relation between $u, v, R, n_1$(rarer medium) and $n_2$(denser medium), where the terms have their usual meaning.$$

A beaker of radius $r$ is filled with water$\left(\text{refractive index} \frac{4}{3}\right)$ up to a height $H$ as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This makes the water surface curved so that the difference in the height of water level at the centre and at the circumference of the beaker is $h\left(h\ll H\text{,} h\ll r\right)$, as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature $R.$ Which of the following is/are correct? ($g$ is the acceleration due to gravity)

A transparent thin film of uniform thickness and refractive index ${\mathrm{n}}_1=1.4$ is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index ${\mathrm{n}}_2=1.5$ , as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then