A YDSE experiment is used to measure the wavelength of light used. The distance between screen and slits is measured by a meter scale with least count 1 mm. The measured distance is 1.500 m. The distance between the slits is measured by a micrometer of least count 0.01 mm. The distance between slits is measured to be 0.33 mm. The fringe width is measured by the same micrometer. It comes out to be 2.50 mm. The wavelength of light is :-

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$330 \pm 28 n m$

$550 \pm 39 n m$

$330 \pm 56 n m$

$550 \pm 19 n m$

answer is A.

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Detailed Solution

$β = \frac{λ D}{d} \Rightarrow λ = \frac{β d}{D} = \frac{2.50 \times 10^{- 3} \times 3.3 \times 10^{- 4}}{1.50}$

$= 550 n m \frac{Δ λ}{λ} = \frac{Δ β}{β} + \frac{Δ d}{d} + \frac{Δ D}{D} = \frac{0.01}{0.33} + \frac{0.01}{2.50} + \frac{10^{- 3}}{1.500} Δ λ = \frac{5.50}{0.33} + \frac{5.5}{2.5} + \frac{0.5.5}{1.50} = \frac{500 + 66 + 11}{30} = \frac{577}{30}$