A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double-slit setup and gives rise to two overlapping interference patterns on the screen. The cen

Question

A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double-slit setup and gives rise to two overlapping interference patterns on the screen. The central maximum of both patterns coincide. Further, it is observed that the third bright fringe of known light coincides with the 4 th bright fringe of the unknown light. From this data, the wavelength of the unknown light is

TestHub · Accepted Answer

For interference, by Young's double slits, the path difference is $\frac{xd}{D} = nλ$ for bright fringes and $\frac{xd}{D} = (2 n + 1) \frac{λ}{2}$ for dark fringes.

The central fringes when $x = 0$ , coincide for all wavelengths.

It is known that the third fringe of $λ_{1} = 590 nm$ coincides with the fourth bright fringe of unknown wavelength $λ$ .

$∴$ $\frac{xd}{D} = 3 \times 590 nm = 4 \times λ nm$

$∴$ $λ = \frac{3 \times 590}{4} = 442.5 nm$

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