Problem

Problem

In Young's double-slit experiment, the wavelength of light was changed from 7000 A˚7000 \text{ \AA} to 3500 A˚3500 \text{ \AA}. While doubling the separation between the slits, which of the following is not true for this experiment? (1) The width of fringes changes. (2) The color of bright fringes changes. (3) The separation between successive bright fringes changes. (4) The separation between successive dark fringes remains unchanged.
Intuitive explanation

When wavelength halves and slit separation doubles, the fringe spacing β=λDd\beta = \frac{\lambda D}{d} shrinks by a factor of four—the numerator drops by half while the denominator doubles. The key insight is tracking how each parameter in the fringe formula changes: smaller wavelength means tighter fringes, larger slit separation means tighter fringes, and these effects multiply. You need to identify which statement about the new setup contradicts this dramatic compression of the interference pattern.

Intuitive explanation

When wavelength halves and slit separation doubles, the fringe spacing β=λDd\beta = \frac{\lambda D}{d} shrinks by a factor of four—the numerator drops by half while the denominator doubles. The key insight is tracking how each parameter in the fringe formula changes: smaller wavelength means tighter fringes, larger slit separation means tighter fringes, and these effects multiply. You need to identify which statement about the new setup contradicts this dramatic compression of the interference pattern.

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