hraghav
- 48
- 5
- Homework Statement
- Light of wavelength λ = 517.4× 10^−9 m is incident on a metal plate that has two thin, parallel slits etched into it a distance of d = 5.44 × 10^−6 m apart. A distance of L=1.29 m away lies a viewing panel onto which the diffraction pattern can be displayed.
The metal plate with the two slits is replaced with a metal plate with a single slit that has a width of a= 3.96 × 10^−6 m. a) What is the ratio of the brightness at y = 1.26 m (from the central fringe) to the brightness of the central fringe?
b) The metal plate with the two slits is replaced with a metal plate with a single slit that has a width of a = 7.96 × 10^-6 m. How far from the central fringe is the 6th dark fringe (destructive interference)?
- Relevant Equations
- a) I = Io(sinβ / β)^2
β = (pi * a*sinθ) / λ
sinθ = y / L
b) asinθ=mλ
a) sinθ = y / L where y = 1.26 m and L = 1.29m
sinθ = 0.9767
β = (pi * a*sinθ) / λ where λ = 517.4 * 10^-9 m and a= 3.96 × 10^−6 m
β = 0.000012151 / 517.4 * 10^-9 = 23.485
I / Io = (sin(23.485) / 23.485)^2
I / Io = 0.0002879
which is 0.2879 * 10^-3
b) asinθ=mλ where m = 6 and λ = 517.4 * 10^-9 m
sinθ = 0.000003104 / a where a = 7.96 × 10^-6 m
sinθ = 0.39
y = Lsinθ. where L = 1.29 m
y = 0.5031 m
which is 50.31 * 10^-2 m
Both these answers are incorrect. Could someone please let me know where am I making an error?
sinθ = 0.9767
β = (pi * a*sinθ) / λ where λ = 517.4 * 10^-9 m and a= 3.96 × 10^−6 m
β = 0.000012151 / 517.4 * 10^-9 = 23.485
I / Io = (sin(23.485) / 23.485)^2
I / Io = 0.0002879
which is 0.2879 * 10^-3
b) asinθ=mλ where m = 6 and λ = 517.4 * 10^-9 m
sinθ = 0.000003104 / a where a = 7.96 × 10^-6 m
sinθ = 0.39
y = Lsinθ. where L = 1.29 m
y = 0.5031 m
which is 50.31 * 10^-2 m
Both these answers are incorrect. Could someone please let me know where am I making an error?