A Level Physics Practice Exam

What causes the path difference to get smaller when the wavelength decreases?

1. The speed of light increases

2. The frequency of light remains constant

3. The angle θ increases

4. The wavelength is shorter

The correct answer is: The wavelength is shorter

The path difference in a wave interference pattern is influenced by the wavelength of the light being used. When the wavelength decreases, the path difference gets smaller due to the fundamental relationship between wavelength and the distance over which a wave travels. Specifically, the path difference arises when waves travel different distances to reach an observer or to interact with other waves. As the wavelength is shorter, for a given angle of incidence or diffraction, the same physical distance corresponds to a smaller fraction of the cycle of the wave. This means that each full wave can be compacted into a shorter space, leading to a smaller path difference between any two points of wavefronts compared to a scenario where the wavelength is longer. Therefore, the reduction in wavelength directly results in a reduction of the phase difference between waves traveling different paths, making the path difference smaller. Other options do not account for the direct relationship between wavelength and path difference. For instance, changes in speed of light or frequency would not directly cause the path difference to decrease solely due to a decrease in wavelength, and an increase in angle would not uniformly decrease path differences without considering the specific geometric arrangement of the experiment. Thus, the relationship is best captured by the concept that shorter wavelengths naturally lead to smaller path differences in wave diffraction or