Final answer:
A diffraction grating with 10,000 lines per centimeter is used to diffract a ray of violet light (wavelength 400 nm). The formula dsin(θ) = mλ is used to find the angles at which there are bright violet rays, in addition to zero degrees. After calculating, it is found that there are bright violet rays at an angle of approximately 23.3 degrees from the perpendicular.
Step-by-step explanation:
A diffraction grating can cause the incident light to split into multiple beams of different wavelengths. The angle at which these beams are observed depends on the properties of the grating and the wavelength of the light. To find the angles at which there are bright violet rays in addition to zero degrees, we need to use the formula:
dsin(θ) = mλ
where d is the grating spacing, θ is the angle of diffraction, m is the order of the diffraction, and λ is the wavelength of the light. In this case, the violet light has a wavelength of 400 nm (0.4 μm) and the grating has 10,000 lines per centimeter (100 lines per millimeter).
Using the given information, we can solve for the angles at which there are bright violet rays:
d = 100 lines/mm = 0.1 mm = 0.1 × 10-3 m
λ = 400 nm = 400 × 10-9 m
Plugging these values into the formula, we get:
(0.1 × 10-3)sin(θ) = m(400 × 10-9)
For the zeroth order diffraction (m = 0), the equation becomes:
(0.1 × 10-3)sin(θ0) = 0(400 × 10-9)
This gives us θ0 = 0 degrees, which is the incident angle.
For the first order diffraction (m = 1), the equation becomes:
(0.1 × 10-3)sin(θ1) = 1(400 × 10-9)
Simplifying, we find:
sin(θ1) = 400 × 10-9 / (0.1 × 10-3) = 0.4
Taking the inverse sine of both sides, we find:
θ1 = sin-1(0.4)
Calculating the value, we find θ1 ≈ 23.3 degrees.
Therefore, there are bright violet rays at an angle of approximately 23.3 degrees from the perpendicular, in addition to zero degrees.