Question

A beam of 568 nm light is incident on a diffraction grating that has 568 lines/mm. Determine the angle of the second-order ray using the diffraction formula. Provide the answer in units of degrees (°).

Answer 1

The angle of the second-order ray for a diffraction grating with 568 lines/mm and 568 nm light is approximately 40.25°, calculated using the formula dsin(θ) = mλ with appropriate conversions and rearrangements.

Step-by-step explanation:

To determine the angle of the second-order ray for the given diffraction grating, we can use the diffraction grating formula:

dsin(θ) = mλ

where:

• d is the distance between adjacent lines on the grating,
• θ is the diffraction angle,
• m is the order of the diffraction maximum (m = 2 for second-order),
• λ is the wavelength of the light (in meters).

First, convert the grating line density to distance between lines:

1 mm = 1 x 10^-3 meters

568 lines/mm = 568 lines/(1 x 10^-3 meters)
d = 1/(568 lines/mm) = 1/(568 x 10^3 lines/m) = 1.76 x 10^-6 meters

Then, insert the known values into the formula and solve for θ. Using 568 nm or 568 x 10^-9 meters for λ:

1.76 x 10^-6 m * sin(θ) = 2 * 568 x 10^-9 m

sin(θ) = (2 * 568 x 10^-9 m) / (1.76 x 10^-6 m)

sin(θ) ≈ 0.6451

θ ≈ sin^-1(0.6451) ≈ 40.25°

Therefore, the angle of the second-order ray is approximately 40.25°.