In the diffraction pattern due to a single slit of width ' a ' with incident light of wavelength ' λ ', at an angle of diffraction ' θ ', the condition for the second max

Question

In the diffraction pattern due to a single slit of width ' a ' with incident light of wavelength ' λ ', at an angle of diffraction ' θ ', the condition for the second maximum is

TestHub · Accepted Answer

For a single slit diffraction pattern, the path difference is given by $Δ x = a sin θ$ .

The condition for the $n$ -th secondary maximum is $Δ x = (2 n + 1) \frac{λ}{2}$ , where $n = 1, 2, 3, \dots$

For the second maximum, $n = 2$ .

Substituting $n = 2$ , we get $a sin θ = (2 (2) + 1) \frac{λ}{2} = \frac{5 λ}{2}$ .

This can be rearranged as $2 a sin θ = 5 λ$ .

Answer: $2 a sin θ = 5 λ$

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