If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 3 0 ∘ in a single slit diffraction pattern

Question

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 3 0 ∘ in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _______ μ m .

TestHub · Accepted Answer

​ θ 1 ​ = sin − 1 ( a 2 λ ​ ) θ 2 ​ = sin − 1 ( a 3 λ ​ ) ∵ θ 1 ​ + θ 2 ​ = 3 0 ∘ ​ ​ ⇒ sin − 1 ( a 2 λ ​ ) + sin − 1 ( a 3 λ ​ ) = 6 π ​ ⇒ a 2 λ ​ 1 − ( a 3 λ ​ ) 2 ​ + a 3 λ ​ 1 + ( a 2 λ ​ ) 2 ​ = sin 6 π ​ ​ Here λ = 628 nm After solving A = 6.07 μ m Approximate Method : ​ θ = θ 1 ​ + θ 2 ​ ⇒ 6 π ​ = a 2 λ ​ + a 3 λ ​ ⇒ 6 π ​ = a 5 ​ ( 628 nm ) ⇒ a = 6 μ m ​

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