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seropon [69]
3 years ago
5

Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is λA = 622nm. The other wavelength is λ

B and is unknown. On a viewing screen, the light with wavelength λA = 622nm produces its third-order bright fringe at the same place where the light with wavelength λB produces its fourth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?
Physics
1 answer:
Sergio039 [100]3 years ago
3 0

Answer:

\lambda_{B}=414.67 nm

Explanation:

In this question we have given

\lambda_{A}=622nm

we have to find

\lambda_{B}=?

We know that

optical path difference for bright fringe is given as=n\lambda

Here,

n is order of fringe

and optical path difference for dark fringe is given as=(n+.5)\lambda

since the light with wavelength \lambda_{A} produces its third-order bright fringe at the same place where the light with wavelength \lambda_{B} produces its fourth dark fringe  

it means

optical path difference for 3rd order bright fringe= optical path difference for forth order dark fringe

Therefore,

3\lambda_{A}=(4+.5)\lambda_{B}...............(1)

Put value of \lambda_{A} in equation (1)

3 \times 622=(4+.5)\lambda_{B}

1866=4.5\lambda_{B}

\lambda_{B}=414.67 nm

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