If the measured angular separation between the second minimum to the left of the central maximum and the third minimu to the right of the central maximum is 30° in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit i

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Solution

Q.
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 30° in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is ________ $μ$ m. [2025]

Ans.
(6)

Angular position of $2^{nd}$ minima $\Rightarrow$ $θ_{1} = (\frac{2 λ}{a})$

Angular position of $3^{rd}$ minima $\Rightarrow$ $θ_{2} = \frac{3 λ}{a}$

$θ = θ_{1} + θ_{2} \Rightarrow \frac{π}{6} = \frac{2 λ}{a} + \frac{3 λ}{a}$

$\frac{π}{6} = \frac{5}{a} (628 nm) \Rightarrow a = 6 μ m$

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