JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Wave Optics

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White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is ______ nm.

Answer: 300

Solution

The first bright fringe of wavelength

λ

lies at

y = \frac{λ D}{d}

, so

λ = \frac{y d}{D}

. With

D = 1.5

m and

d = 0.3 \times 1 0^{- 3}

λ_{v} = \frac{2.0 \times 1 0 ^{- 3} \times 0.3 \times 1 0 ^{- 3}}{1.5} = 4.0 \times 1 0^{- 7} m, λ_{r} = \frac{3.5 \times 1 0 ^{- 3} \times 0.3 \times 1 0 ^{- 3}}{1.5} = 7.0 \times 1 0^{- 7} m

The two wavelengths are

400

nm and

700

nm, so they differ by

300

nm.

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Integer answer

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