Final answer:
A semiconductor laser emits light at 400.0 nm and is passed through a grating with 1,000 lines etched over a space of 10.00 mm. We can calculate the angle of diffraction for first and second order diffraction, as well as determine the wavelength of light for a given angle of diffraction. The magnitude of the angle of diffraction would be the same regardless of the direction of propagation.
Step-by-step explanation:
A semiconductor laser emits light at 400.0 nm. The light is passed through a grating where 1,000 lines are etched covering a space of 10.00 mm. The light is directed directly at the grating.
(a) To calculate the angle the light beam diffracts for first order diffraction, we can use the formula: sin(θ) = /, where is the order of diffraction, is the wavelength, and is the spacing between the lines. Plugging in the values, we have sin(θ) = (1)(400.0 nm)/(10.00 mm). Solving for θ, we get θ ≈ 0.829°.
(b) To calculate the angle the light beam diffracts for second order diffraction, we can use the same formula but with = 2. Plugging in the values, we have sin(θ) = (2)(400.0 nm)/(10.00 mm). Solving for θ, we get θ ≈ 1.659°.
(c) To calculate the wavelength of light produced by a laser with a first order angle of diffraction of 23.9°, we can rearrange the formula to solve for : = sin(θ)/. Plugging in the values, we have = (10.00 mm)sin(23.9°)/(1). Solving for , we get ≈ 4.55 nm.
(d) If a new grating with the spacing between the lines doubled were to replace the previous one, the new angle for part (a) can be calculated using the formula: sin(θ) = (1)(400.0 nm)/(20.00 mm). Solving for θ, we get θ ≈ 0.415°.
(e) The magnitude of the angle of diffraction would be the same whether going left or right because diffraction does not depend on the direction of propagation.