Wave Optics

Question

In a single slit diffraction experiment, a slit of width 'd' is illuminated by red light of wavelength 650 nm. For what value of 'd' will
(i) the first minimum fall at an angle of diffraction of 30°, and
(ii) the first maximum fall at an angle of diffraction of 30°?

Solution

Given, width of the slit is 'd'.
Wavelength of red light,

λ

= 650 nm = 650

650 \times 10^{- 9} m

(i) Angle of diffraction,

θ = 30^{o}

(given)

For, first minimum fall

λ = d \sin θ o r, nλ = d sinθ

\Rightarrow

650 = d \sin 30 °

\Rightarrow

650 = d \times \frac{1}{2}

i.e.,

d = 1300 nm .

(ii) For, first maximum fall at the same angle of diffraction,

(2 n + 1) \frac{λ}{2} = d \sin θ

i.e.,

3 λ = 2 d \sin θ

\Rightarrow

3 \times 650 = 2 d \sin θ = 2 d \sin 30 °

\Rightarrow

1950 = 2 d \times \frac{1}{2}

i.e.,

d = 1950 nm .

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