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  4. In Youngs double slit experiment, light waves of wavelength 5.4 × 102 nm and 68.5 × 101 nm are used in turn, keeping the same geometry of the set up. The ratio of the fringe widths in two cases is

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Q. In Youngs double slit experiment, light waves of wavelength $5.4 \times 10^2 \,nm$ and $68.5 \times 10^1\, nm$ are used in turn, keeping the same geometry of the set up. The ratio of the fringe widths in two cases is

Wave Optics

Solution:

$Fringe \,width, \beta = \frac{D\lambda}{d} $
$\therefore \frac{\beta_{1}}{\beta_{2}} = \frac{\lambda_{1}}{\lambda_{2}} $
$=\frac{ 5.4\times10^{2}}{68.5\times10^{1}} = 7.9$