Kumar Mittal Solutions for Exercise 2: For DIFFERENT COMPETITIVE EXAMINATIONS

In figure, the optical fibre is $l= 2 \mathrm{m}$ long and has a diameter of $d=20 \mathrm{\mu m}$. If a ray of light is incident on one end of the fibre at angle ${\theta }_1=40°$, the number of reflection it makes before emerging from the other end is close to : (refractive index of fibre is $1.31$ and $\sin 40°=0.64$)

A transparent cube, made of a material of refractive index $n_2$, is immersed in a liquid of refractive index $n_1(n_1<n_2)$. A ray is incident on the face $AB$ at an angle $\theta$ (shown in the figure). Total internal reflection takes place at point $E$ on the face $BC$.

Then $\theta$ must satisfy:

In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?

Pick the wrong answer in the context with rainbow.

A light wave is incident normally on a glass slab of refractive index $1.5$. If $4\%$ of light gets reflected and the amplitude of the electric field of the incident light is $30 \raisebox{1ex}{$\mathrm{V}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.$, then the amplitude of the electric field for the wave propagating in the glass medium will be:

A concave mirror has a radius of curvature of $40 \mathrm{cm}$. It is at the bottom of a glass that has water filled up to $5 \mathrm{cm}$ (see figure). If a small particle is floating on the surface of the water, its image as seen, from directly above the glass, is at a distance d from the surface of the water. The value of d is close to: (Refractive index of water $=1.33$)

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence of $45°$. The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air, select the possible value(s) of $n$ from the following:

A transparent slab of thickness d has a refractive index $n\left(z\right)$ that increases with $z$. Here $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2(>n_1)$, as shown in the figure. A ray of light is incident with angle ${\theta }_i$ from medium $1$ and emerges in medium $2$ with refraction angle ${\theta }_f$ with a lateral displacement $l$.

Which of the following statements are true?