JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Geometrical Optics

A ray of light AO in vacuum is incident on a glass slab at angle

6 0^{\circ}

and refracted at angle

3 0^{\circ}

along OB as shown in the figure. The optical path length of light ray from

A

B

is:

(A) $2 a + \frac{2 b}{3}$
(B) $2 a + \frac{2 b}{3}$
(C) $\frac{2 3}{a} + 2 b$
(D) $2 a + 2 b$ ✓ Correct

Answer: (D)

Solution

Snell's law at the surface gives

sin 6 0^{\circ} = μ sin 3 0^{\circ}

, i.e.

\frac{3}{2} = μ \cdot \frac{1}{2}

, so

μ = 3

. Geometrically the ray travels

A O = \frac{a}{c o s 6 0 ^{\circ}} = 2 a

in vacuum and

O B = \frac{b}{c o s 3 0 ^{\circ}} = \frac{2 b}{3}

in the glass. The optical path length is

A O + μ \cdot O B = 2 a + 3 \cdot \frac{2 b}{3} = 2 a + 2 b

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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