A slit 0.019 mm wide is illuminated with red light (=680 nm). How wide is the central maximum? Side maxima? - how wide is the central maximum
A slot 0019 mm (which is 1.9 x 10 ^ -5? Touched with the conversion) wide is illuminated with red light (= 680 nm). What is the width of the central maximum of the diffraction pattern on a screen 1.1 m from the site and the maximum width is the side of the diffraction pattern? (My teacher wants the answer in cm.)
Saturday, February 13, 2010
How Wide Is The Central Maximum A Slit 0.019 Mm Wide Is Illuminated With Red Light (=680 Nm). How Wide Is The Central Maximum? Side Maxima?
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Gap width: a = 19 microns
Wavelength: λ = 680 nm = 0.68 microns
Distance d = 1.1 m = 110 cm
In each column experiment, the amplitude of the electric field of
Light on the direction α is calculated as the superposition
Amplitudes of the small elements of DX from the slot.
Eo dE dx = exp (2πi R (x) / λ) =
Eo = exp (2πi [x sin α] / λ) dx
E (α) = integral [-a / 2 .. 2 +] in Eo exp (2πi [x sin α] / λ) dx =
Int = [-a / 2 .. + A / 2] 1 / (2πi) λ / sena Eo exp (2πi [x sin α] / λ) d [2πisinα / x λ]] =
= Int [πiasinα / λ .. + Πiasinα / λ] 1 / (2πi) λ / sena Eo exp (z) dz =
-1 / Π Λ / sena sin (a sign of π / λ) Eo
The intensity of the A (α) of light is proportional to the square of the eclectic
Area E (α):
A (α) = 1/ ² Π (λ / sena) ² sin ² (SENA πa / λ) ² = Ao Eo (λ / sena) ² sin ² (SENA πa / λ)
Intensity minima occur when
n sena πa / λ = π, n = 1,2,3 ...
For small angles α = tanα sena
Answer:
Central maximum Hc n =- 1 n = 1
HC 2αd = λ = 2d / a = 7,87 cm
Maxima of n = 1 to n = 2
HC = αd λ = d / a = 3.94 cm
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