Question

What are the angular positions of the first and second minima in a diffraction pattern produced by a slit of width 0.20 mm that is illuminated by 400 nm light? What is the angular width of the central peak?

Answer 1

The angular positions of the first and second minima in a diffraction pattern are found using the formula θ = arcsin(mλ / a), where m is the order of the minimum, λ is the wavelength, and a is the slit width. The angular width of the central peak is twice the angle of the first minimum.

Step-by-step explanation:

The question involves calculating the angular positions of the first and second minima in a diffraction pattern and determining the angular width of the central peak.

To find the angles for the minima, we can use the single-slit diffraction formula: θ = arcsin(mλ / a), where θ is the angular position, m is the order of the minimum, λ is the wavelength of light, and a is the width of the slit.

For a slit width of 0.20 mm and light of 400 nm wavelength, the angular positions for the first (m=1) and second (m=2) minima are found by plugging these values into the formula:

1. First minimum: θ1 = arcsin((1)(400 x 10-9) / (0.20 x 10-3))
2. Second minimum: θ2 = arcsin((2)(400 x 10-9) / (0.20 x 10-3))

To calculate the angular width of the central peak, we double the angle of the first minimum, which gives θ = 2 x θ1.