First slide

Diffraction

Question

A parallel beam of light of wavelength 6000 A is incident normally on a slit of width 0.2 mm. The diffraction pattern is obsessed or a screen which is placed at the focal plane of a convex lens of focal length 50 cm. If the lens is pl,aced dose to the slit, the distance between the minima om both sides of central maximum will be

Moderate

A

1 mm
B

2 mm
C

3mm
D

4mm

Solution

The angular separation of minima on both side of central maximum of single slit is 2 $θ$ where e is given by
$esin θ = λ or \sin θ = λ / d \sin θ = \frac{6000 \times 10^{- 10}}{0 .2 \times 10^{- 3}} = 3 \times 10^{- 3} or θ \approx 3 \times 10^{- 3} rad (∵ \sin θ \approx θ) when tho lens is placed close to the slit, then x = ftan θ \approx fθ wherc x is the distarce of ftst minlmum from the contral maximum . The distance between two minima on both sides of ceDtral maximum is 2 x = 2 fθ = 2 \times 0 \cdot 5 \times (3 \times 10^{- 3}) = 3 \times 10^{- 3} m = 3 mm$

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