#### Question

Show that the angular width of the first diffraction fringe is half that of the central fringe.

#### Solution

Let* λ* and *a* be the wavelength and slit width of diffracting system, respectively. Let O be the position of central maximum. Condition for the first minimum is given by

asinθ=mλ .....(1)

Let *θ* be the angle of diffraction.

As diffraction angle is small

∴ sinθ ≈ θ

For the first diffraction minimum, let *θ = θ*_{1}* *

For the first minimum, take *m* =1

aθ_{1}=λ

`=>theta_1=lambda/a`

Now, angular width AB = *θ*_{1}

Angular width BC = *θ*_{1}

Angular width AC = 2*θ*_{1}

Width of central maximum = 2*θ*_{1}

Is there an error in this question or solution?

Solution Show that the Angular Width of the First Diffraction Fringe is Half that of the Central Fringe. Concept: Interference of Light Waves and Young’S Experiment.