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 $${{3H} \over 4}{\left( {1 + {{{\omega ^2}H} \over {4g}}} \right)^{ - 1}}$$
2
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
A
H2 > H1
B
H3 > H1
C
0.85 cm < (H2 $$ - $$ H1) < 0.9 cm
D
H2 > H3
3
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in the figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1 = n2 = n. The focal length is f + $$\Delta $$f when n1 = n and n2 = n + $$\Delta $$n.
Assuming $$\Delta $$n << (n - 1) and 1 < n < 2, the correct statement(s) is/are
A
If $${{\Delta n} \over n} < 0$$ then $${{\Delta f} \over f}$$ > 0
B
For n = 1.5, $$\Delta $$n = 10-3 and f = 20 cm, the value of $$\left| {\Delta f} \right|$$ will be 0.02 cm (round off to 2nd decimal place).
The relation between $${{{\Delta f} \over f}}$$ and $${{{\Delta n} \over n}}$$ remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.
4
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $$f,$$ as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)
