What should be the width of each slit to obtain n maxima of double sli

1.	What should be the width of each slit to obtain n maxima of double slit pattern within the central maxima of single slit pattern?
Answer» Let 'a' be the width of each slit. Linear separation between n bright fringes, x = nβ = \(\frac{n\lambda D}{d}\) Corresponding angular separation, θ₁ = \(\frac{\mathrm{x}}{D}=\frac{n\lambda}{d}\) Now, the angular width of central maximum in the diffraction pattern of a single slit, θ₂ = \(\frac{2\lambda}{a}\) As θ₁ = θ₂ \(\frac{n\lambda}{d}=\frac{2\lambda}{a}\) \(\therefore\)a = \(\frac{2d}{n}\); where d = separation between slits \(\frac{n\lambda}{d}=\frac{2\lambda}{a}\) \(n=\frac{2d}{a}\) ,where d is separation between slit and a width of slit.

What should be the width of each slit to obtain n maxima of double slit pattern within the central maxima of single slit pattern?

Answer»

Let 'a' be the width of each slit.

Linear separation between n bright fringes, x = nβ = \(\frac{n\lambda D}{d}\)

Corresponding angular separation, θ₁ = \(\frac{\mathrm{x}}{D}=\frac{n\lambda}{d}\)

Now, the angular width of central maximum in the diffraction pattern of a single slit,

θ₂ = \(\frac{2\lambda}{a}\)

As θ₁ = θ₂

\(\frac{n\lambda}{d}=\frac{2\lambda}{a}\)

\(\therefore\)a = \(\frac{2d}{n}\); where d = separation between slits

\(\frac{n\lambda}{d}=\frac{2\lambda}{a}\)

\(n=\frac{2d}{a}\) ,where d is separation between slit and a width of slit.

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