First slide

Diffraction

Question

A slit of width a is illuminated by white light. For red light $(λ = 6500 Å)$ the first minima is obtained at $θ = 30^{\circ} .$ Then the value of a will be

Moderate

A

$3250 Å$
B

$6.5 \times 10^{- 4} mm$
C

1.24 microns
D

$2.6 \times 10^{- 4} cm$

Solution

For first minima $θ = \frac{λ}{a} or a = \frac{λ}{θ}$
$∴ a = \frac{6500 \times 10^{- 8} \times 6}{π} (As 30^{\circ} = \frac{π}{6} radian)$
$= 1.24 \times 10^{- 4} cm = 1.24 microns$

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