The Intensity of Second Order Secondary Maxima in Fraunhofer Single Slit Diffraction

In Fraunhofer single slit diffraction, when a monochromatic light wave passes through a single slit, it diffracts and creates a pattern of bright and dark regions on a screen. The central maximum is the principal maximum, and the secondary maxima occur on either side of it.

The intensity of the principal maximum is denoted as I0. We need to find the intensity of the second-order secondary maxima.

Explanation:

1. Intensity Distribution in Single Slit Diffraction:
When a monochromatic light wave passes through a single slit, it diffracts and creates a diffraction pattern on a screen. The intensity of the resulting pattern is given by the formula:

I = I0 * (sinθ/θ)^2

where I is the intensity at a particular angle θ, and I0 is the intensity of the principal maximum (at θ = 0).

2. Location of Secondary Maxima:
The secondary maxima occur at angles where the intensity is a minimum (dark regions) in the diffraction pattern. The first secondary maximum is located at an angle θ1, given by:

sinθ1 = λ / (2 * a)

where λ is the wavelength of the light and a is the width of the slit.

Similarly, the second-order secondary maximum is located at an angle θ2, given by:

sinθ2 = 2 * sinθ1 = 2 * λ / a

3. Intensity of Second Order Secondary Maxima:
To find the intensity of the second-order secondary maximum, we substitute the value of θ2 into the intensity formula:

I2 = I0 * (sinθ2 / θ2)^2

Substituting the value of θ2, we get:

I2 = I0 * ((2 * λ / a) / (2 * λ / a))^2
= I0 * (1)^2
= I0

Therefore, the intensity of the second-order secondary maximum is equal to the intensity of the principal maximum, which is I0.

Conclusion:
The correct answer is option 'A' - I0 / 62.5. The intensity of the second-order secondary maximum in Fraunhofer single slit diffraction is equal to the intensity of the principal maximum, which is I0.

Intensity of n^th order secondary maxima