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In a Young's double slit experiment, slits are separated by 0.5 mm and the screen is placed 1.5 m away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is -

1. 5.6 mm
2. 7.8 mm
3. 9.75 mm
4. 15.6 mm

Correct answer: 7.8 mm

Solution

The least distance where the bright fringes coincide for two wavelengths can be found using the formula for fringe positions, which depends on the wavelength and the slit separation. By calculating the least common multiple of the fringe positions for both wavelengths, we find that the first coinciding bright fringe occurs at 7.8 mm from the central maximum.

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