Question

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

Answer 1

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)

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

$1866=4.5\lambda_{B}$

$\lambda_{B}=414.67 nm$