Respuesta :
The angle measured in degrees at which the 2nd-order bright fringe located is located is; 58.78°
What is the angle of the diffraction grating?
Formula for diffraction grating is; dsinθ = mλ
where;
d = grating spacing = 1/(3000 lines per cm) = 1/3 × 10⁻⁵ m
m = order of fringe
λ = wavelength of light = 550 nm = 550 × 10⁻⁹ m.
Now, tanθ = x/D
where;
x = distance of nth order fringe from central maximum.
D = distance of screen from grating = 115 cm = 1.15 m
Now sinθ = d/mλ
θ is small and so we can approximate as sinθ ≅ tanθ
Thus;
d/mλ = x/D
for a second order bright fringe, m = 2.
d/2λ = x/D
x = dD/2λ
For a dark fringe, we have
d/(m + 1/2)λ = x'/D
where;
x' is the distance of the fringe from the central maximum.
For a second-order dark fringe, m = 2. Thus;
d/(2 + 1/2)λ = x'/D
d/(5/2)λ = x'/D
2d/5λ = x'/D
x' = 2dD/5λ
So, the distance between the 2nd order bright fringe and the 2nd dark fringe is; x" = dD/2λ - 2dD/5λ
x" = dD/10λ
Plugging in the values of the variables, we have;
x" = 1/3 × 10⁻⁵ m × 1.15 m/(10 × 550 × 10⁻⁹ m)
x" = 1.15/165 × 10² m
x" = 0.697 m
x'' = 69.7 cm
Thus;
tan θ = x/D = 115/69.7
θ = tan⁻¹(115/69.7)
θ = 58.78°
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