For a diffraction grating with 500 lines per mm, what is the angle of the first

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Question: For a diffraction grating with 500 lines per mm, what is the angle of the first order maximum for light of wavelength 600 nm?

Options:

Correct Answer: 30 degrees

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.

For a diffraction grating with 500 lines per mm, what is the angle of the first order maximum for light of wavelength 600 nm?

For a diffraction grating with 500 lines per mm, what is the angle of the first order maximum for light of wavelength 600 nm?

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).
Step 9: Calculate θ to find that θ ≈ 30 degrees.

Diffraction Grating – A device that disperses light into its component wavelengths using the principle of interference.
Grating Equation – The relationship d sin θ = nλ, where d is the distance between grating lines, θ is the angle of diffraction, n is the order of the maximum, and λ is the wavelength of light.
Order of Maximum – The integer n that indicates the sequence of the maxima in the diffraction pattern.