Ray Optics · JEE Advanced previous year questions

Two identical concave mirrors each of focal length $f$ are facing each other as shown in the schematic diagram. The focal length $f$ is much larger than the size of the mirrors. A glass slab of thickness $t$ and refractive index $n_0$ is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source $S$ is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on $S$ itself, which of the following distances between the two mirrors is/are correct:

1. A.$4f+\left(1-\frac{1}{n_0}\right)t$
2. B.$2f+\left(1-\frac{1}{n_0}\right)t$
3. C.$4f+(n_0-1)t$
4. D.$2f+(n_0-1)t$

1. A.For $n=1.42$, $h=50\text{ cm}$.
2. B.For $n=1.35$, $h=36\text{ cm}$.
3. C.For $n=1.45$, $h=65\text{ cm}$.
4. D.For $n=1.48$, $h=85\text{ cm}$.

A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence ${\theta }_0$. The ray partially refracts into the sphere with angle of refraction ${\varphi }_0$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in List-I with their values in List-II and choose the correct option. $$\begin{array}{ll}\text{List-I}& \text{List-II}\\ \text{(P) If }n=2\text{ and }\alpha =180^{\circ }\text{, then all the possible values of }{\theta }_0\text{ will be}& \text{(1) }30^{\circ }\text{ and }{0}^{\circ }\\ \text{(Q) If }n=\sqrt{3}\text{ and }\alpha =180^{\circ }\text{, then all the possible values of }{\theta }_0\text{ will be}& \text{(2) }60^{\circ }\text{ and }{0}^{\circ }\\ \text{(R) If }n=\sqrt{3}\text{ and }\alpha =180^{\circ }\text{, then all the possible values of }{\varphi }_0\text{ will be}& \text{(3) }45^{\circ }\text{ and }{0}^{\circ }\\ \text{(S) If }n=\sqrt{2}\text{ and }{\theta }_0=45^{\circ }\text{, then all the possible values of }\alpha \text{ will be}& \text{(4) }150^{\circ }\\ & \text{(5) }{0}^{\circ }\end{array}$$

1. A.$\mathrm{P}\to 5;\mathrm{Q}\to 2;\mathrm{R}\to 1;\mathrm{S}\to 4$
2. B.$\mathrm{P}\to 5;\mathrm{Q}\to 1;\mathrm{R}\to 2;\mathrm{S}\to 4$
3. C.$\mathrm{P}\to 3;\mathrm{Q}\to 2;\mathrm{R}\to 1;\mathrm{S}\to 4$
4. D.$\mathrm{P}\to 3;\mathrm{Q}\to 1;\mathrm{R}\to 2;\mathrm{S}\to 5$

1. A.The blue light is polarized in the plane of incidence.
2. B.The angle of the prism is $45^{\circ }$.
3. C.The refractive index of the material of the prism for red light is $\sqrt{2}$.
4. D.The angle of refraction for blue light in air at the exit plane of the prism is $60^{\circ }$.

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10\pm 0.1\mathrm{cm}$ and the distance of its real image from the lens is $20\pm 0.2\mathrm{cm}$. The error in the determination of focal length of the lens is $n\%$. The value of $n$ is ____.

1. A.It will deflect up by an angle ${\tan }^{-1}\left[\frac{(n_2^2-n_1^2)d}{2h}\right]$.
2. B.It will deflect up by an angle ${\tan }^{-1}\left[\frac{(n_2-n_1)d}{h}\right]$.
3. C.It will not deflect.
4. D.The deflection angle depends only on $(n_2-n_1)$ and not on the individual values of $n_1$ and $n_2$.