JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Wave Optics

Two light waves having the same wavelength

λ

in vacuum are in phase initially. Then the first wave travels path

L_{1}

through a medium of refractive index

n_{1}

while the second wave travels a path of length

L_{2}

through a medium of refractive index

n_{2}

. After this the phase difference between the two waves is:

(A) $\frac{2 π}{λ} (\frac{L _{2}}{n _{1}} - \frac{L _{1}}{n _{2}})$
(B) $\frac{2 π}{λ} (\frac{L _{1}}{n _{1}} - \frac{L _{2}}{n _{2}})$
(C) $\frac{2 π}{λ} (n_{1} L_{1} - n_{2} L_{2})$ ✓ Correct
(D) $\frac{2 π}{λ} (n_{2} L_{1} - n_{1} L_{2})$

Answer: (C)

Solution

The phase a wave accumulates is set by its optical path, the refractive index times the geometrical length travelled. The first wave gathers optical path

n_{1} L_{1}

and the second

n_{2} L_{2}

, so the optical path difference between them is

n_{1} L_{1} - n_{2} L_{2}

. Multiplying by

\frac{2 π}{λ}

, with

λ

the vacuum wavelength, gives the phase difference

\frac{2 π}{λ} (n_{1} L_{1} - n_{2} L_{2})

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option

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JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Wave Optics

Solution

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