Respuesta :
Answer:
Explanation:
Width of each slit d = 1 x 10⁻² / 7300
= 1.37 x 10⁻⁶ m
Distance of screen D = 3.6 m
for light of wavelength λ = 410 nm = 410 x 10⁻⁹ m
position of first maxima =λ D / d
= 410 x 10⁻⁹ x 3.6 / 1.37 x 10⁻⁶
= 1077.37 x 10⁻³ m
= 1.077 m
for light of wavelength λ = 750 nm = 750 x 10⁻⁹ m
position of first maxima =λ D / d
= 750 x 10⁻⁹ x 3.6 / 1.37 x 10⁻⁶
= 1438.54 x 10⁻³ m
= 1.438 m
width of first order spectrum = 1.438 - 1.077 m
= .361 m
36.1 cm .
The width of the first-order spectrum on a screen 3.60 m away is;
1.13 m
We are given;
Minimum wavelength; λ_min = 410 nm = 410 × 10⁻⁹ m
Maximum wavelength; λ_max = 750 nm = 750 × 10⁻⁹ m
Grating; d = 7300 slits/cm = 0.01/7300 m = 1.3699 × 10⁻⁶ m
Distance; r = 3.2 m
Let us find the angle of the first wavelength with the formula;
θ = sin⁻¹(mλ/d)
first wavelength has an order of m = 1
Thus; θ = sin⁻¹(1 * 410 × 10⁻⁹/(1.3699 × 10⁻⁶))
θ = sin⁻¹0.2993
θ₁ = 17.42°
For the second wavelength;
sin θ = [(0.2993 × 750 × 10⁻⁹)/(410 × 10⁻⁹)
sin θ = 0.5475
θ = sin⁻¹0.5475
θ₂ = 33.2°
Thus; the width of spectrum is;
3.6(tan 33.2 - tan 17.42)
width of spectrum = 1.13 m
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