Answer:
423nm
Explanation:
To find the unknown wavelength you take into account the distance y to the maximum central fringe, for light fringes and dark fringes.
- for light fringes:
[tex]dsin\theta=m\lambda\\\\sin\theta\approx\theta=\frac{y}{D}\\\\y=\frac{m\lambda_1D}{d}[/tex]
- for dark fringes:
[tex]y=\frac{m\lambda_2/2 D}{d}[/tex]
The third-order bright fringe (m= 3) of wavelength A coincides with the fourth dark fringe (m=4) of the wavelength B. Hence you have that:
[tex]\frac{(3)\lambda_1D}{d}=\frac{(4)\lambda_2D}{d}\\\\\lambda_2=\frac{3}{4}\lambda_1=\frac{3}{4}(564nm)=423nm[/tex]
hence, the wavelength B is 423nm
Answer:
The unknown wavelength is 376 nm
Explanation:
We are given two parallel slits that are illuminated by light composed of two wavelengths, λa = 564 nm and the other λb which is unknown.
On a viewing screen, the light whose wavelength is known produces its third dark fringe at the same place where the light with wavelength B produces its fourth dark fringe.
For the wavelength A: (bright fringes)
sinθ = mλa/d
where m = 3
sinθ = 3λa/d
For the wavelength B: (dark fringes)
sinθ = (m + ½)λb/d
where m = 4
sinθ = (4 + ½)λb/d
Since we both fringes are produced at the same place,
3λa/d = (4 + ½)λb/d
d cancels out
3λa = (4 + ½)λb
λb = 3λa/(4 + ½)
λb = 3(564)/(4.5)
λb = 376 nm
Therefore, the other wavelength is 376 nm.
