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 = 613 nm. The other wavelength is ?B and is unknown. On a viewing screen, the light with wavelength ?A = 613 nm produces its fifth-order bright fringe at the same place where the light with wavelength ?B produces its sixth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?

From Physics cutwell and johnson 9th edition.

please explain very detailed and mention the importance of order of the bright fringe and the number of dark fringe.

thanks

Explanation / Answer

The condition for bright fringe is

Y1 = mLR/d

here L is wave length , R is distance between width and screen

for first wave length

Y1 = 4( 619nm)* R/d

for second wave length use condtion of dark fringe

Y2 = ( m'+1/2) LR/d

sixth dark fringe mans m' = 5

Y2= ( 5+ 1/2) L_B R/d

Y2 = 5.5 * L_B* R/d

here Y1 = Y2

5* 613 nm * R/d = 5.5 * L_B* R/d

L_B = 557.27 nm

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