In Young's double slit experiment, zero order and 10th order bright fringes are obtained at distances of 11.50 mm and 14.50 mm from some reference point. Wavelength of light used is 6000 Å. If wavelength of light becomes 5000 Å, find the positions of zero order and 10th order bri

Question

In Young's double slit experiment, zero order and 10th order bright fringes are obtained at distances of 11.50 mm and 14.50 mm from some reference point. Wavelength of light used is 6000 Å. If wavelength of light becomes 5000 Å, find the positions of zero order and 10th order bright fringes for the same arrangement.

Accepted Answer

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> [!TLDR]
> $\beta=0.30$ mm at 6000 A. Since $\beta\propto\lambda$, at 5000 A $\beta'=0.25$ mm. Central fringe unchanged (11.50 mm); 10th bright fringe at 14.00 mm.
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> **Fringe width from the data:** The zero-order and 10th-order bright fringes are at $11.50$ mm and $14.50$ mm, so ten fringe widths span $3.00$ mm:
> $$\beta=\frac{14.50-11.50}{10}=0.30	ext{ mm}\quad(\lambda=6000	ext{ A}).$$
>
> **New wavelength 5000 A:** Since $\beta=\dfrac{\lambda D}{d}\propto\lambda$ (same $D,d$):
> $$\beta'=\beta	imes\frac{\lambda'}{\lambda}=0.30	imes\frac{5000}{6000}=0.25	ext{ mm}.$$
> …

Concept understanding — Fringe Width in Young's Double Slit Experiment

Fringe width and source separation

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