light of wavelength 5×100000 is incident normally on a plane transmission grating of width 3 cm and 15000 lines, find the angle of diffraction in first order
Answers
Answer:
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Explanation:
Diffraction grating: d sinθn = nλ where n is an integer
λ=5.30×10
−7
m
When n = 1, θ1 = 15.4°
Slit separation, d =
sinθ
1
λ
=
sin15.4
o
5.30×10
−7
= 1.996×10
−6
m
When n =2
slit separation d =
sinθ
2
λ
⟹sinθ
2
=
d
λ
⟹θ
o
=sin
−1
(
1.996×10
−6
5.30×10
−7
)
⟹θ
2
=16.7
o
the angle of diffraction in the first order for this case is 0.019 degrees.
To Find:
to find the angle of diffraction (θ) in the first order (m = 1) for a given set of conditions.
Given:
The wavelength of the incident light (λ) is 5 x 100000 nm
The width of the plane transmission grating (d) is 3 cm and it has 15000 lines.
The angle of incidence (θi) is normal incidence (90 degrees)
Solution:
The angle of diffraction in the first order can be found using the grating equation:
θ = (mλ) / (d sin θi)
where θ is the angle of diffraction, m is the order of diffraction (m = 1 for first order), λ is the wavelength of the incident light, d is the distance between the lines on the grating (in this case, 3 cm / 15000 = 0.0002 cm), and θi is the angle of incidence (which is 90 degrees for normal incidence).
Plugging in the given values, we get:
θ = (1 * (5 x 100000 x 10^-9 m)) / (0.0002 cm x sin 90) = 0.0000333 radians
To convert this to degrees, we can use the conversion factor:
1 radian = 57.3 degrees
So,
θ = 0.0000333 radians * 57.3 degrees/radian = 0.019 degrees
So the angle of diffraction in the first order for this case is 0.019 degrees.
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