When monochromatic light of wavelength 5.0 x 10^-7 m is incident normally on a plane diffraction grating, the second order diffraction lines are formed at angles of 300 to the normal to the grating. What is the number of lines per millimeter of the grating?

Explanation

To solve this problem, we use the formula for diffraction grating: d sin(θ) = nλ, where d is the grating spacing, θ is the angle of diffraction, n is the order of diffraction, and λ is the wavelength.Given: λ = 5.0 × 10-7 m, θ = 30°, and n = 2.Substitute these values into the formula to find d: d = nλ / sin(θ) = (2 × 5.0 × 10-7) / 0.5 = 2 × 10-6 m.The number of lines per meter is the reciprocal of d: N = 1/d = 1/(2 × 10-6) = 500,000 lines/m.Converting to lines per millimeter: N = 500,000 / 1,000 = 500 lines/mm.Therefore, Option B is correct. The other options result from incorrect calculations or misunderstandings of the formula.