干涉：練習題

Which condition must be met for two sources of waves to be considered coherent?

In a Young's double-slit experiment, monochromatic light of wavelength $$ 600 \text{ nm} $$ is used. The slits are separated by $$ 0.50 \text{ mm} $$ , and the distance from the slits to the screen is $$ 2.0 \text{ m} $$ . What is the fringe spacing, $$ w $$ , observed on the screen?

In a double-slit experiment, the slits are separated by $$s = 0.20 \text{ mm}$$ , and the screen is $$D = 1.5 \text{ m}$$ away. The third-order bright fringe is measured to be $$11.25 \text{ mm}$$ from the central maximum. Calculate the wavelength $$\lambda$$ of the light used.

If two coherent waves of wavelength $$ \lambda $$ meet at a point after travelling paths that differ by a path difference of $$ (n + 1/2)\lambda $$ , where $$ n $$ is an integer $$ (n = 0, 1, 2, ...) $$ , what type of interference occurs?

White light is used in a double-slit experiment. What is the characteristic appearance of the central maximum on the screen?

In the context of wave interference, what two conditions must sources satisfy to be considered coherent?

Two coherent sources of light with wavelength \(540 \text{ nm}\) meet at a point where the path difference is \(1.89 \mu\text{m}\). Determine the phase difference between the waves in radians and the type of interference occurring at this point.

When light reflects from the two surfaces of a thin film, interference occurs. Explain why, even if the thickness of the film is negligible, the reflected rays may still show destructive interference.

In a Young's double-slit experiment, monochromatic light is used. The slit separation is \(s = 0.40\, \mathrm{mm}\), and the distance between the slits and the screen is \(D = 2.0\, \mathrm{m}\). The observed fringe spacing is \(w = 3.15\, \mathrm{mm}\).

a) State two requirements for the light sources used in Young's experiment to ensure a clear, sustained interference pattern. (2 points)

b) Calculate the wavelength, \(\lambda\), of the monochromatic light used. Give your answer in nanometers. (2 points)

A Young’s double-slit experiment is performed using a light source that emits two discrete wavelengths: \(\lambda_A = 480\, \text{nm}\) and \(\lambda_B = 640\, \text{nm}\). The distance between the slits is \(0.250\, \text{mm}\) and the screen is placed \(1.80\, \text{m}\) from the slits.

a) Calculate the fringe spacing on the screen for the interference pattern produced by \(\lambda_B\).
b) Determine the minimum non-zero distance from the central maximum at which a bright fringe of \(\lambda_A\) coincides exactly with a bright fringe of \(\lambda_B\).