Question

A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates young's double lit and gives rise to two overlapping interference patterns on the screen. the central maximum of both lights coincide. further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. from this data, the wavelength of the unknown light is

Answer 1

Hey There!!

This question related to the concepts of Young's Double Slit Experiment



Here, we will use only one concept:

Path Difference for $n^{th}$ bright fringe = $n\lambda$


Here, let us name:

Known wavelength = $\lambda_1$ = 590 nm
Unknown wavelength = $\lambda_2$


We are given that the Central Maxima of both lights coincide. This means that there is no initial path difference between the two lights.

Now, third bright fringe of known wavelength light coincides with the fourth bright fringe of the unknown wavelength light.

So, we can write:

$3\lambda_1 = 4\lambda_2 \\ \\ \implies 3\times 590 = 4\lambda_2 \\ \\ \implies \lambda_2 = \frac{3\times 590}{4} \\ \\ \implies \boxed{\lambda_2=442.5 \, \,nm}$


Hope it helps
Purva
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