For a diffraction grating with 500 lines per mm, what is the angle of the first order maximum for light of wavelength 600 nm?
Practice Questions
1 question
Q1
For a diffraction grating with 500 lines per mm, what is the angle of the first order maximum for light of wavelength 600 nm?
30 degrees
45 degrees
60 degrees
15 degrees
Using the grating equation d sin θ = nλ, where d = 1/500000 m, n = 1, and λ = 600 x 10^-9 m, we find θ ≈ 30 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: For a diffraction grating with 500 lines per mm, what is the angle of the first order maximum for light of wavelength 600 nm?
Solution: Using the grating equation d sin θ = nλ, where d = 1/500000 m, n = 1, and λ = 600 x 10^-9 m, we find θ ≈ 30 degrees.
Steps: 9
Step 1: Understand the problem. We need to find the angle of the first order maximum (n=1) for light with a wavelength of 600 nm using a diffraction grating with 500 lines per mm.
Step 2: Convert the number of lines per mm to the distance between the lines (d). Since there are 500 lines in 1 mm, d = 1 mm / 500 = 0.002 mm = 2 x 10^-6 m.
Step 3: Convert the wavelength from nanometers to meters. 600 nm = 600 x 10^-9 m.
Step 4: Use the grating equation: d sin θ = nλ. Here, d = 2 x 10^-6 m, n = 1, and λ = 600 x 10^-9 m.
Step 5: Substitute the values into the equation: (2 x 10^-6) sin θ = 1 * (600 x 10^-9).
Step 6: Simplify the equation: sin θ = (600 x 10^-9) / (2 x 10^-6).
Step 7: Calculate sin θ: sin θ = 0.3.
Step 8: Find θ by taking the inverse sine: θ = sin^(-1)(0.3).
