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    Question

    In a Young’s double slit experiment, a glass plate is

    introduced in front of one slit. The central fringe shifts but the fringe width remains unchanged. What does this indicate?
    A Phase difference changes but path difference does not Correct Answer Incorrect Answer
    B Path difference changes but fringe spacing depends only on geometry Correct Answer Incorrect Answer
    C Optical path is unaffected Correct Answer Incorrect Answer
    D Wavelength changes due to medium Correct Answer Incorrect Answer

    Solution

    Given information:

    • A glass plate is introduced in front of one of the slits
    • The central fringe shifts
    • The fringe width remains unchanged
    Analysis: 1.     Effect on central fringe position: When light passes through the glass plate, it travels slower than in air. This increases the optical path length for the light passing through that slit. The result is that the path difference between the two slits changes, which causes the central fringe (where path difference is normally zero) to shift. 2.     Effect on fringe width: The fringe width (distance between adjacent bright or dark fringes) is given by: β = λD/d Where: o    λ is the wavelength o    D is the distance to the screen o    d is the separation between slits Since the fringe width remains unchanged, this means the wavelength, screen distance, and slit separation remain effectively the same. The key insight is that the glass plate changes the optical path length (and thus the phase) for one beam, but it doesn't change the basic geometry of the experiment or the wavelength in the region where interference occurs (after the slits). Therefore, option (b) is correct: Path difference changes but fringe spacing depends only on geometry. The glass plate introduces a path difference, shifting the entire fringe pattern, but the spacing between fringes (fringe width) remains unchanged because it depends only on the wavelength and geometric parameters (D and d) which are unaffected.

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