What is the angle of incidence?
Whatever it is, use the diffraction equation with orders n=1 and n=2.
The width of the grating won't matter.
Whatever it is, use the diffraction equation with orders n=1 and n=2.
The width of the grating won't matter.
sin(θ) = mλ / d
Where:
- θ is the angle of diffraction.
- m is the order of the diffraction (m = 0 for the zeroth order, m = ±1 for the first orders, m = ±2 for the second orders, and so on).
- λ is the wavelength of light.
- d is the spacing between the slits in the diffraction grating.
In this case, the diffraction grating has a width of 1.0 cm, which means the spacing between the slits (d) is given by:
d = 1.0 cm / 1000
Since the wavelength of light is given as 550 nm, we can convert it to meters:
λ = 550 nm * (1 meter / 10^9 nm)
Now we can calculate the angles for the first two diffraction orders:
For the first order (m = 1):
sin(θ₁) = (1 * 550 nm * (1 meter / 10^9 nm)) / (1.0 cm / 1000)
For the second order (m = 2):
sin(θ₂) = (2 * 550 nm * (1 meter / 10^9 nm)) / (1.0 cm / 1000)
To find the actual values of θ₁ and θ₂, we need to take the inverse sine (arcsine) of these quantities.
Calculating the angles will give you the angles of the first two diffraction orders.