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Chapter 6: Problem 50

Explain the importance of the Young double-slit experiment.

Short Answer

Expert verified
The importance of the Young double-slit experiment lies in its demonstration of the wave-particle duality of light and the interference of light waves. The experiment involves a monochromatic light source passing through two parallel slits, which then diffracts and interferes, creating a pattern of alternating light and dark bands on a screen. This interference pattern provides evidence for the wave nature of light, as particles would not create such a pattern. Furthermore, the experiment has contributed to the development of quantum mechanics by demonstrating that both light and particles like electrons display both wave-like and particle-like properties.

Step by step solution

01

Introduce the Young double-slit experiment

The Young double-slit experiment, named after Thomas Young who first performed it in 1801, is a landmark experiment which demonstrates the wave-particle duality of light. In this experiment, a light source passes through a pair of thin parallel slits, then the light diffracts and ultimately forms a pattern on a screen. This pattern is due to the interference of light waves.
02

Explain the experimental setup

A monochromatic light source (light of single wavelength) is directed towards a barrier with two slits, separated by a certain distance. As the light passes through these slits, it diffracts and spreads out in all directions. These light waves then overlap in the region behind the slits and interfere. Finally, a screen is placed at a specific distance from the double slits to capture the pattern generated by this interference of light waves.
03

Explain the interference pattern

When the light waves from the two slits overlap, they interfere with each other, producing a pattern of alternating light and dark bands on the screen. This is called an interference pattern. The light bands occur when the light waves from the two slits are in phase (constructive interference) and reinforce each other, while the dark bands occur when the light waves are out of phase (destructive interference) and cancel each other out.
04

Calculate the position of bright and dark bands

The position of the bright and dark bands can be calculated by using the interference formula: \[n\lambda = d\sin\theta\] Where: - \(n\) is an integer representing the order of the bright band (0, 1, 2, ...) - \(\lambda\) is the wavelength of the light source - \(d\) is the distance between the two slits - \(\theta\) is the angular position of the bright band on the screen For dark bands, the formula is slightly different: \[(n+\frac{1}{2})\lambda = d\sin\theta\]
05

Explain the significance of the Young double-slit experiment

The significance of the Young double-slit experiment lies in the fact that it provides evidence for the wave nature of light, as particles would not create an interference pattern. Furthermore, the experiment demonstrates the wave-particle duality of light, as light exhibits both wave-like and particle-like properties. This idea was later extended to particles such as electrons, leading to the development of quantum mechanics. Thus, the Young double-slit experiment plays a foundational role in our understanding of the behavior of light and quantum mechanics.

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