AP Physics 2 Exam Question:

A beam of light with a wavelength of 632.8 nm passes through two narrow slits that are separated by a distance of 0.1 mm. The resulting interference pattern is observed on a screen located 2.0 meters away from the slits.

a) Calculate the angular separation between the first and second order bright fringes in the resulting interference pattern.

b) Determine the distance between the first order bright fringe and the central maximum on the screen.

c) Explain why the distance between the slits and the screen affects the observed interference pattern.

Answer:

a) To calculate the angular separation between the first and second order bright fringes, we can use the formula:

θ = λ / d

where θ is the angular separation, λ is the wavelength of light, and d is the distance between the two slits.

Given: Wavelength (λ) = 632.8 nm = 632.8 × 10^(-9) m Distance between slits (d) = 0.1 mm = 0.1 × 10^(-3) m

Using the formula, we have:

θ = (632.8 × 10^(-9)m) / (0.1 × 10^(-3)m) = 6.328 × 10^(-3) rad

Therefore, the angular separation between the first and second order bright fringes is 6.328 × 10^(-3) radians.

b) To determine the distance between the first order bright fringe and the central maximum, we can use the formula:

y = λL / d

where y is the distance between the first order bright fringe and the central maximum, L is the distance between the slits and the screen, and d is the distance between the two slits.

Given: Wavelength (λ) = 632.8 nm = 632.8 × 10^(-9) m L = 2.0 meters Distance between slits (d) = 0.1 mm = 0.1 × 10^(-3) m

Using the formula, we have:

y = (632.8 × 10^(-9)m) × (2.0 m) / (0.1 × 10^(-3)m) = 12.656 meters

Therefore, the distance between the first order bright fringe and the central maximum on the screen is 12.656 meters.

c) The distance between the slits and the screen affects the observed interference pattern because it determines the angular separation between the fringes. As the distance (L) increases, the angular separation (θ) between the fringes decreases. This means that the interference pattern becomes more spread out with wider fringes as the screen is moved further away from the slits. Conversely, if the screen is brought closer to the slits, the interference pattern becomes more compressed with narrower fringes. This phenomenon arises from the wave nature of light and can be explained by the principles of diffraction and interference.