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
2
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
3
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 $${{3H} \over 4}{\left( {1 + {{{\omega ^2}H} \over {4g}}} \right)^{ - 1}}$$
4
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure.
Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3 m). If H1, H2, and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are
