If light of wavelength 500 nm passes through a diffraction grating with 1000 lin

If light of wavelength 500 nm passes through a diffraction grating with 1000 lines/mm, what is the angle for the first-order maximum?

If light of wavelength 500 nm passes through a diffraction grating with 1000 lines/mm, what is the angle for the first-order maximum?

Step 1: Understand the problem. We need to find the angle for the first-order maximum when light of wavelength 500 nm passes through a diffraction grating with 1000 lines/mm.
Step 2: Convert the wavelength from nanometers to meters. 500 nm = 500 x 10^-9 m.
Step 3: Calculate the distance 'd' between the grating lines. Since there are 1000 lines/mm, we convert this to meters: 1000 lines/mm = 1000 x 10^3 lines/m. Therefore, d = 1 / (1000 x 10^3) m = 1 x 10^-6 m.
Step 4: Use the grating equation d sin(θ) = mλ. Here, m = 1 for the first-order maximum, λ = 500 x 10^-9 m, and d = 1 x 10^-6 m.
Step 5: Substitute the values into the equation: (1 x 10^-6) sin(θ) = 1 x (500 x 10^-9).
Step 6: Simplify the equation: sin(θ) = (500 x 10^-9) / (1 x 10^-6).
Step 7: Calculate sin(θ): sin(θ) = 0.5.
Step 8: Find θ by taking the inverse sine: θ = sin^(-1)(0.5).
Step 9: Calculate θ, which gives approximately 30 degrees.

Diffraction Grating – The phenomenon where light spreads out as it passes through a grating, leading to interference patterns.
Grating Equation – The relationship d sin(θ) = mλ, where d is the distance between grating lines, θ is the angle of the maximum, m is the order of the maximum, and λ is the wavelength of light.
First-Order Maximum – The first bright fringe observed in a diffraction pattern, corresponding to m=1 in the grating equation.