Two parallel slits are illuminated by light composed of two wavelengths. One wav

Question

Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is ?A = 630 nm. The other wavelength is ?B and is unknown. On a viewing screen, the light with wavelength ?A = 630 nm produces its fifth-order bright fringe at the same place where the light with wavelength ?B produces its fifth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?
The correct answer is 700 nm but i dont know how they got that answer. please help.

Explanation / Answer

let R is the distance between screen and slits

d is the slits separtion

for lamda_A wave

for nth bright fringe, yn = n*lamda*R/d

for 5th order bright fringe = 5*lamda_A*R/d ---(1)

for lamda_B wave

for n the dark fringe, yn = (2*n-1)*lamda*R/d

for 5th order dark fringe = (2*5 - 1)lamda_B*R/(2*d)

= 9*lamda_B*R/(2*d) ---(2)

now equate the two equations

9*lamda_B*R/(2*d) = 5*lamda_A*R/d

lamda_B = (10/9)*lamda_A

= (10/9)*630 nm

= 700 nm <<<<<<<<<--------------------Answer

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