JEE Advanced 2019 · Paper 2 · Physics Q6

← JEE Advanced 2019 · Paper 2

PhysicsMultiple correct+4 / -1Question 6 of 54

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 $H_1$ , $H_2$ , and $H_3$ are the apparent depths of a point $X$ on the bottom of the three cylinders, respectively, the correct statement(s) is/are:

Three glass cylinders of height H side by side: I with a flat top, II with a convex (outward-bulging) top, III with a concave top; X marks the centre of each base.

H_2 > H_1

H_3 > H_1

H_2 > H_3

0.8\text{ cm} < (H_2 - H_1) < 0.9\text{ cm}

Answer and worked solution

Official answer: A, C

Refraction from glass ( $n=1.5$ ) into air at the top surface:
$\frac1v-\frac{1.5}u=\frac{1-1.5}R,$
with $u=-30$ cm, taking upward as positive.

Flat top: $H_1=\dfrac{30}{1.5}=20$ cm.
Convex top (centre of curvature below, $R=-300$ cm): $\dfrac1v=-0.05+0.00167$ , so $H_2=20.69$ cm.
Concave top ( $R=+300$ cm): $\dfrac1v=-0.05-0.00167$ , so $H_3=19.35$ cm.

So $H_2>H_1>H_3$ :

(A) is true and (C) is true.
(B) is false.
(D) $H_2-H_1=0.69$ cm, not between 0.8 and 0.9 cm. False.

(A), (C)

Topics:Refraction at spherical surfaces Refraction at plane surfaces

← Previous question Next question →

JEE Advanced 2019 · Paper 2, Physics question 6