(II) Suppose a thin piece of glass is placed in front of the lower slit in Fig. 34–7 so that the two waves enter the slits 180° out of phase (Fig. 34–44). Describe in detail the interference pattern on the screen.

검증된 단계별 안내

Understand the setup: The problem involves a double-slit interference experiment where a thin piece of glass is placed in front of the lower slit. This introduces a phase difference of 180° (or π radians) between the two waves entering the slits. This phase difference will affect the interference pattern on the screen.

Recall the principle of interference: In a double-slit experiment, the interference pattern on the screen is determined by the constructive and destructive interference of the waves from the two slits. Constructive interference occurs when the path difference between the waves is an integer multiple of the wavelength (nλ), while destructive interference occurs when the path difference is an odd multiple of half the wavelength ((2n+1)λ/2).

Account for the phase shift: The 180° phase shift introduced by the glass effectively inverts the conditions for constructive and destructive interference. This means that points on the screen that would normally experience constructive interference will now experience destructive interference, and vice versa.

Describe the new pattern: The central maximum (bright fringe) in the original pattern will now become a dark fringe due to the phase shift. Similarly, the positions of all other bright and dark fringes will be swapped. The spacing between the fringes will remain the same, as it depends on the wavelength of the light and the geometry of the setup, which are unchanged.

Summarize the result: The interference pattern on the screen will appear inverted compared to the original pattern. Bright and dark fringes will exchange places, but the overall spacing and symmetry of the pattern will remain unchanged.

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주요 개념

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Wave Interference

Wave interference occurs when two or more waves overlap and combine to form a new wave pattern. This can result in constructive interference, where waves are in phase and amplify each other, or destructive interference, where waves are out of phase and cancel each other out. Understanding this concept is crucial for analyzing how waves interact, particularly in the context of light waves passing through slits.

Phase Difference

Phase difference refers to the difference in the phase of two waves at a given point in time. In this scenario, a phase difference of 180° means that the waves are completely out of phase, leading to destructive interference. This concept is essential for predicting the resulting intensity pattern on the screen, as it determines whether the waves will reinforce or cancel each other.

Interference Pattern

An interference pattern is the pattern of light and dark regions created on a screen when waves interfere with each other. In the case of the glass causing a 180° phase shift, the resulting pattern will show dark fringes where destructive interference occurs, indicating points of cancellation. This pattern is a direct visual representation of the wave behavior and is fundamental in experiments like the double-slit experiment.