Question

Two parallel slits are illuminated by light composed of two wavelengths, one of which is 657 nm. On a viewing screen, the light whose wavelength is known produces its third dark fringe at the same place where the light whose wavelength is unknown produces its fourth-order bright fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength

Answer 1

λ = 5.75 10⁻⁷ mm

Step-by-step explanation:

This is a slit interference exercise, we analyze each wavelength separately

λ = 657 nm indicate that the third dark pattern

a sin θ = (m + ½) lam

a sin θ = (3 + ½) 657 10⁻⁹

a sin θ = 2299.5 10⁻⁹ nm

for the other wavelength in the same place we have m = 4 bright

a sin θ = m lam

we substitute

2299.5 10⁻⁹ = 4 λ

λ =
`(2299.5 \ 10^9 )/( 4)`

λ = 5.75 10⁻⁷ mm