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Question: A narrow slit of width 2 nm is illuminated by monochromatic light of wavelength 500 nm. The distance...

A narrow slit of width 2 nm is illuminated by monochromatic light of wavelength 500 nm. The distance the first minima on either side on a screen at a distance of 1 m is :

A

5 nm

B

0.5 nm

C

1 nm

D

10 nm

Answer

0.5 nm

Explanation

Solution

: here a=2mm=2×10−3ma = 2mm = 2 \times 10^{- 3}m

λ=500nm=500×10−9m=5×10−7m\lambda = 500nm = 500 \times 10^{- 9}m = 5 \times 10^{- 7}m

D = 1m

The distance between the first minima on either side on a screen is

=2λDa=2×5×10−7×12×10−3= \frac{2\lambda D}{a} = \frac{2 \times 5 \times 10^{- 7} \times 1}{2 \times 10^{- 3}}

=5×10−4m=0.5×10−3m=0.5mm= 5 \times 10^{- 4}m = 0.5 \times 10^{- 3}m = 0.5mm