At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is [2015]

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Solution

Q.
At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is [2015]

1 $π$ radian

2 $\frac{π}{8}$ radian

3 $\frac{π}{4}$ radian

4 $\frac{π}{2}$ radian

Ans.
(1)

The situation is shown in the figure.

In figure A and B represent the edges of the slit AB of width $a$ and C represents the midpoint of the slit.

For the first minimum at P,

$a \sin θ = λ$ ...(i)

where $λ$ is the wavelength of light.

The path difference between the wavelets from A to C is

$Δ x = \frac{a}{2} \sin θ = \frac{1}{2} (a \sin θ) = \frac{λ}{2} (using (i))$

The corresponding phase difference $Δ ϕ$ is

$Δ ϕ = \frac{2 π}{λ} Δ x = \frac{2 π}{λ} \times \frac{λ}{2} = π$

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