Respuesta :
Answer:
1)At 24.2°, 30.5°, 35.3°, and 41.7°, the wavelengths are 409.9 nm, 507.5 nm, 577.9 nm and 665.2 nm respectively.
A) at 23.80°, wavelength = 403.5 nm
B) at 30.2°,wavelength = 503 nm
Explanation:
1) Order of maxima in the question is m=1
θ1 = 24.2°
θ2 = 30.5°
θ3 = 35.3°
θ4 = 41.7°
Equation for mth order maxima is;
d sinθ = mλ
Where d is the separation lines between grating and λ is the wavelength
From the question, the grating has 10,000 lines per cm
Thus, d = 1/10000 = 0.0001 cm then converting it to meters, d= 0.0001 x 10^-(2) = 10^-(6)
So,
Wavelength(λ) for θ1 = 24.2°;
dsinθ = mλ
m = 1 and so :λ = dsinθ
λ = 10^-(6) x sin 24.2 = 409.9 x 10^(-9) m or simply 409.9 nm
Wavelength(λ) for θ2 = 30.5°;
dsinθ = λ;
λ = 10^-(6) x sin 30.5 = 507.5 nm
Wavelength(λ) for θ3 = 35.3°;
dsinθ = λ;
λ = 10^-(6) x sin 35.3 = 577.9 nm
Wavelength(λ) for θ4 = 41.7°;
dsinθ = λ;
λ = 10^-(6) x sin 41.7 = 665.2 nm
A) At 23.8°;
dsinθ = λ;
λ = 10^-(6) x sin sin 23.8 = 403.5 nm
B) At 30.2°;
dsinθ = λ;
λ = 10^-(6) x sin sin 23.8 = 503 nm
