In Young's double slit experiment the two slits are 0 . 6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on

Question

In Young's double slit experiment the two slits are 0 . 6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be _____ nm .

TestHub · Accepted Answer

According to the question, the first dark fringe is observed directly opposite to one of the slits. Therefore, half of the fringe width is equal to half of the distance between the slits.

$\frac{β}{2} = \frac{d}{2} \Rightarrow β = d = 6 mm$

$\Rightarrow \frac{λ D}{d} = 0.6 \times 10^{- 3} \Rightarrow λ = \frac{0.6 \times 10^{- 3} d}{D} \Rightarrow λ = \frac{0.6 \times 10^{- 3} \times 0.6 \times 10^{- 3}}{80 \times 10^{- 2}}$

$\Rightarrow λ = 450 \times 10^{- 9} m = 450 nm$

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