Question:

A light wave is incident on a double slit, producing an interference pattern on a screen located 1.5 meters away. The distance between the slits is 0.2 mm and the distance from the central maximum to the first-order maximum is measured to be 5.1 cm. The light source generates monochromatic light with a wavelength of 525 nm.

a) Calculate the distance between the slits and the screen, in meters.

b) Determine the angular separation between the central maximum and the first-order maximum.

c) Comment on what will happen to the interference pattern on the screen if the wavelength of the light is doubled.

Answer:

a) The distance from the central maximum to the first-order maximum, also known as the fringe spacing, can be calculated using the formula:

d = (λL) / s

where d is the fringe spacing, λ is the wavelength of light, L is the distance from the slits to the screen, and s is the slit separation.

Given: λ = 525 nm = 525 × 10⁻⁹ m d = 5.1 cm = 5.1 × 10⁻² m

Rearranging the formula, we can solve for L:

L = (d * s) / λ

L = ((5.1 × 10⁻² m) * (0.2 × 10⁻³ m)) / (525 × 10⁻⁹ m)

L = 0.194 m

Therefore, the distance between the slits and the screen is approximately 0.194 meters.

b) The angular separation between the central maximum and the first-order maximum can be calculated using the formula:

θ = tan^(-1)(y/L)

where θ is the angular separation, y is the fringe spacing, and L is the distance from the slits to the screen.

Given: y = 5.1 cm = 5.1 × 10⁻² m L = 1.5 m

Substituting the values into the formula, we find:

θ = tan^(-1)((5.1 × 10⁻² m) / (1.5 m))

θ ≈ 2.04 degrees

Therefore, the angular separation between the central maximum and the first-order maximum is approximately 2.04 degrees.

c) If the wavelength of the light is doubled, the fringe spacing (d) in the interference pattern will also double. This is because the fringe spacing is directly proportional to the wavelength of the light. As a result, the interference pattern on the screen will have a larger fringe spacing, meaning the fringes will be farther apart. This will result in a less dense interference pattern with larger and more spread-out fringes.