Question

Light of wavelength 573.0 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 63.5 cm from the slit. The distance on the screen between the second order minimum and the central maximum is 2.03 cm . What is the width of the slit in micrometers (μm)?

Answer 1

The width of the slit, as calculated from the diffraction pattern data using the single-slit diffraction formula, is 35.7 micrometers (μm).

Step-by-step explanation:

To calculate the width of the slit in micrometers using the diffraction pattern data provided, we can use the formula for the position of the minima in a single-slit diffraction pattern, which is given as y = (mλL) / a, where y is the distance from the central maximum to the m-th order minimum, m is the order of the minimum, λ is the wavelength of the light, L is the distance from the slit to the screen, and a is the slit width. In this case, we're looking for the distance to the second-order minimum, so m = 2. Given values are λ = 573.0 nm = 573.0 x 10-9 m, L = 63.5 cm = 0.635 m, and y = 2.03 cm = 0.0203 m.

Rearranging the formula to solve for the slit width a, we get:

a = (mλL) / y

Plugging in the numbers:

a = (2 x 573.0 x 10-9 m x 0.635 m) / 0.0203 m

a = 35.7 x 10-6 m or 35.7 µm