The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 µm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringes width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

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The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 µm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringes width is 1 cm, what is slit separation distance?

(i.e. distance between the centres of each slit.)

25 µm

75 µm

50 µm

100 µm

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$∴$ sin 30° = $\frac{λ}{a} \Rightarrow$ λ = 0.5 µm

Later,

β = $\frac{Dλ}{d} \Rightarrow d = \frac{Dλ}{β}$ = 25 µm