AP Physics 2 Exam Question

Question:

A student is studying the quantum phenomenon known as wave-particle duality. They perform an experiment to investigate the behavior of light. The experimental setup consists of a double-slit apparatus, where a beam of light passes through two narrow slits. The light source emits green light with a wavelength of 550 nm. The distance between the slits is 0.02 mm, and the distance from the slits to a screen is 1.0 m. When the experiment is conducted in a dark room, an interference pattern is observed on the screen.

a) Explain the concept of wave-particle duality in the context of the double-slit experiment.

b) Calculate the separation between adjacent bright fringes on the screen.

Answer:

a) The concept of wave-particle duality suggests that particles like photons can exhibit both wave-like and particle-like behavior. In the double-slit experiment, the photons interfere with each other and create an interference pattern similar to what is observed in wave phenomena. This wave-like behavior is observed when the photons pass through the two slits and interfere constructively or destructively. On the other hand, the photons also behave as particles because they can be detected as discrete points on the screen. This duality between wave and particle nature of photons is a fundamental concept in quantum mechanics.

b) To calculate the separation between adjacent bright fringes on the screen, we can use the equation for the path difference between the two interfering waves:

Where:

• $\Delta x$ is the separation between adjacent bright fringes,
• $\lambda$ is the wavelength of light (550 nm = 550 × 10^(-9) m),
• $L$ is the distance from the slits to the screen (1.0 m),
• $d$ is the distance between the slits (0.02 mm = 0.02 × 10^(-3) m).

Substituting the given values into the equation:

Therefore, the separation between adjacent bright fringes on the screen is 27.5 mm.