A slit of width 'd' is illuminated by white light. For what value of 'd' is the first minimum for red light of λ = 650 nm located at point P. For what value of the wavelength of light will the first diffraction maxima also fall at P?

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Solution

Given, width of the slit = d
Wavelength,

λ

= 650 nm

At first minimum, n = 1
∴ d sin 30° = nλ

\Rightarrow

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

i.e.,

d = 1300 nm

For first maxima to be at P

d \sin θ = \frac{3}{2} λ'

\Rightarrow

λ' = \frac{2 d \sin ϕ}{3} = \frac{2 \times 1300 \times \sin 30 °}{3} nm

= 433.3 nm.

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