Question

Light of wavelength 560 m passes through a diffraction grating, and a first-order maximum (m = 1) is

observed on a screen at an angle of 20 degrees from the center of the screen.
1. At what angle will the second-order maximum be observed?
2. How many lines per millimeter does the grating have?

Answer 1

To find the angle for the second-order maximum, we need to use the equation for the diffraction grating. We can use the information about the first-order maximum to find the distance between adjacent slits and then use that value to find the angle for the second-order maximum. The grating has approximately 50.76 lines per millimeter.

Step-by-step explanation:

To find the angle for the second-order maximum, we need to use the equation for the diffraction grating:

dsinθ = mλ

Where d is the distance between adjacent slits on the diffraction grating, θ is the angle of the maximum, m is the order of the maximum, and λ is the wavelength of the light.

In this case, we know that the first-order maximum is observed at an angle of 20 degrees, so we can use this information to find the distance between adjacent slits:

d = λ/sintθ

Substituting the values, we get:

d = (560 x 10^-9 m) / sin(20°) = 1.970 x 10^-5 m

Now, we can use this value to find the angle for the second-order maximum:

dsinθ = mλ

(1.970 x 10^-5 m)sinθ = (2) * (560 x 10^-9 m)

θ = sin^(-1)((2) * (560 x 10^-9 m) / (1.970 x 10^-5 m)) ≈ 56.2°

Therefore, the angle for the second-order maximum will be approximately 56.2 degrees.

To find the number of lines per millimeter on the grating, we can use the formula:

N = 1/d

Where N is the number of lines per millimeter and d is the distance between adjacent slits in millimeters. Substituting the value for d, we get:

N = 1 / (1.970 x 10^-5 m) ≈ 50.76 lines per millimeter

Therefore, the grating has approximately 50.76 lines per millimeter.