JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Geometrical Optics

Three glass cylinders of equal height

H = 30 cm

and same refractive index

n = 1.5

are placed on a horizontal surfaces 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

(A) $H_{3} > H_{1}$
(B) $0.8 cm < (H_{2} - H_{1}) < 0.9 cm$
(C) $H_{2} > H_{3}$ ✓ Correct
(D) $H_{2} > H_{1}$ ✓ Correct

Answer: (C), (D)

Solution

For cylinder I (flat top):

H_{1} = \frac{H}{n} = \frac{30}{1.5} = 20

cm = 0.2 m.

For cylinder II (convex top), using refraction formula:

\frac{1}{v} + \frac{3}{2 H} = \frac{- 1}{2 ( - 3 )}

Solving:

v = - \frac{6}{29}

m, so

H_{2} = \frac{6}{29}

m ≈ 0.207 m.

For cylinder III (concave top):

\frac{1}{v} + \frac{3}{2 H} = \frac{- 1}{2 ( 3 )}

Solving:

v = - \frac{6}{31}

m, so

H_{3} = \frac{6}{31}

m ≈ 0.194 m.

Therefore:

H_{3} < H_{1} < H_{2}

, so options (C) and (D) are correct.

H_{2} - H_{1} = \frac{6}{29} - \frac{6}{30} \approx 0.0068

m = 0.68 cm, which is not in the range (0.8, 0.9) cm. Option (B) is incorrect.

JEE Advanced · 2019 · 27 May 2019 · Paper 2 · One or more correct options

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JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Geometrical Optics

Solution

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