How to Calculate the Width of a Single Slit Using Diffraction Patterns

How can we determine the width of a single slit using diffraction patterns?

A helium-neon laser (λ = 633 nm) illuminates a single slit and is observed on a screen 1.30 m behind the slit. The distance between the first and second minima in the diffraction pattern is 3.95 mm. What is the width (in mm) of the slit?

Calculation Method for Determining the Width of a Single Slit

The width of the slit is approximately 0.052 mm, calculated using the formula for single-slit diffraction patterns.

To calculate the width of the slit, we can use the formula for the separation between two adjacent minima in a single-slit diffraction pattern:

d * sin(θ) = m * λ

Here, d represents the width of the slit, θ is the angle of the diffraction pattern, m is the order of the minima (in this case, m = 1 for the first minimum), and λ is the wavelength of the laser light.

First, we need to find the angle θ. Since the screen is located at a distance of 1.30 m from the slit, we can consider a right-angled triangle formed by the slit, the screen, and the central maximum of the diffraction pattern. The opposite side of this triangle is the distance between the first and second minima, which is given as 3.95 mm. The hypotenuse is the distance from the slit to the screen, which is 1.30 m.

By dividing the opposite side by the hypotenuse, we can find the value of sin(θ):

sin(θ) = opposite / hypotenuse = 3.95 mm / 1.30 m

Next, we substitute the known values into the formula and solve for the width of the slit:

d * sin(θ) = m * λ

d * (3.95 mm / 1.30 m) = 1 * 633 nm

Rearranging the equation and solving for d, we get:

d = (1 * 633 nm) / (3.95 mm / 1.30 m)

Therefore, the width of the slit is approximately 0.052 mm.