A 1.0cm wide diffraction grating has 1000slits. It is illuminated by light of wavelength 550nm. What are the angles of the first two diffraction orders?

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.

To calculate the angles of the first two diffraction orders, we can use the formula:

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.