A diffraction grating has a length of 1.1 cm and contains 1.7e4 lines. Calculate the first order diffraction angle for light with a wavelength of 448 nm. Give you answer in degrees. Anyone know??
That's n*lambda = d*sin theta.
n = 1
lambda is given
d = distance between lines. Wouldn't that be 1.1 cm/1.7e4 = ?
Make sure cm and nm are in same units.
To calculate the first order diffraction angle for light using a diffraction grating, we can use the formula:
sin θ = nλ / d
where θ is the diffraction angle, n is the order of diffraction, λ is the wavelength of light, and d is the spacing between the grating lines.
Given:
Length of the grating (d) = 1.1 cm = 0.011 m
Number of lines (N) = 1.7e4
Wavelength of light (λ) = 448 nm = 448e-9 m
Order of diffraction (n) = 1
To calculate the spacing between the grating lines (d), we can use the formula:
d = L / N
where L is the length of the grating and N is the number of lines.
Plugging in the values:
d = 0.011 m / 1.7e4
Calculating the value of d:
d ≈ 6.47e-7 m
Now we can calculate the diffraction angle (θ):
sin θ = (1 * 448e-9 m) / 6.47e-7 m
Calculating the value of sin θ:
sin θ ≈ 0.00692086
To find the angle θ, we can take the inverse sine (sin⁻¹) of the value:
θ ≈ sin⁻¹(0.00692086)
Calculating the angle θ:
θ ≈ 0.397°
Therefore, the first order diffraction angle for light with a wavelength of 448 nm through the given diffraction grating is approximately 0.397°.