AP Physics 2 Exam Question

Wave Optics

A student is performing an experiment to study interference patterns produced by a double-slit setup. The separation between the slits is 0.1 mm, and the distance from the slits to the screen is 2.0 m. The student uses a laser with a wavelength of 650 nm shining through the double slits.

1. Calculate the distance between the central maximum and the first-order maximum on the screen.

Answer:

The distance between the central maximum and the first-order maximum can be found using the formula:

Y = (λL) / d

Where:

• Y is the distance between the central maximum and the first-order maximum on the screen
• λ is the wavelength of the laser (in meters)
• L is the distance from the slits to the screen (in meters)
• d is the separation between the slits (in meters)

Given information:

• λ = 650 nm = 650 × 10^(-9) m
• L = 2.0 m
• d = 0.1 × 10^(-3) m

Substituting the given values into the formula:

Y = (650 × 10^(-9) m × 2.0 m) / (0.1 × 10^(-3) m)

Simplifying the expression:

Y = 13 × 10^(-3) m = 13 mm

Therefore, the distance between the central maximum and the first-order maximum on the screen is 13 mm.

Note: The interference pattern created by a double-slit setup consists of a central maximum (where the two waves from the slits constructively interfere) and several higher-order maxima (produced by constructive interference of waves arriving at different angles). The distance between the central maximum and the first-order maximum can be determined using the formula provided.