Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l>0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.
Which of the following statement(s) is(are) correct?
A
The ray of light will come out for $\theta=30^{\circ}$, for $0< l < L$.
B
There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
C
The ray of light will NEVER come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
D
The ray of light will come out for $\theta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.
2
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
For a prism of prism angle $$\theta$$ = 60$$^\circ$$, the refractive indices of the left half and the right half are, respectively, n1 and n2 (n2 $$\ge$$ n1) as shown in the figure. The angle of incidence i is chosen such that the incident light rays will have minimum deviation if n1 = n2 = n = 1.5. For the case of unequal refractive indices, n1 = n and n2 = n + $$\Delta$$n (where $$\Delta$$n << n), the angle of emergence e = i + $$\Delta$$e. Which of the following statement(s) is(are) correct?
A
The value of $$\Delta$$e (in radians) is greater than that of $$\Delta$$n
B
$$\Delta$$e is proportional to $$\Delta$$n
C
$$\Delta$$e lies between 2.0 and 3.0 milliradians, if $$\Delta$$n = 2.8 $$\times$$ 10$$-$$3
D
$$\Delta$$e lies between1.0 and 1.6 milliradians, if $$\Delta$$n = 2.8 $$\times$$ 10$$-$$3
3
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
A wide slab consisting of two media of refractive indices n1 and n2 is placed in air as shown in the figure. A ray of light is incident from medium n1 to n2 at an angle $$\theta$$, where sin$$\theta$$ is slightly larger than 1/n1. Take refractive index of air as 1. Which of the following statement(s) is(are) correct?
A
The light ray enters air if n2 = n1
B
The light ray is finally reflected back into the medium of refractive index n1 if n2 < n1
C
The light ray is finally reflected back into the medium of refractive index n1 if n2 > n1
D
The light ray is reflected back into the medium of refractive index n1 if n2 = 1
4
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A beaker of radius r is filled with water (refractive index $${4 \over 3}$$) 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 center and at the circumference of the beaker is h (h << H, h << r), 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
$$R = {{{h^2} + {r^2}} \over {2h}}$$
B
$$R = {{3{r^2}} \over {2h}}$$
C
Apparent depth of the bottom of the beaker is close to $${{3H} \over 2}\left( {1 + {{{\omega ^2}H} \over {2g}}} \right)^{-1}$$
D
Apparent depth of the bottom of the beaker is close to $${{3H} \over 4}{\left( {1 + {{{\omega ^2}H} \over {4g}}} \right)^{ - 1}}$$
