A wavelength of 540 nm yields a first-order maximum at 13.4° with a grating.At what angle will the second-order maximum appear for this wavelength?
A)No second-order maximum exists in this case.
B)90°
C)-13°
D)28°
E)1.16°

Question

Quizplus · Accepted Answer

We can use the grating equation:

n*λ = d*sin(θ)

where n is the order, λ is the wavelength, d is the grating spacing, and θ is the angle of diffraction.

For the first-order maximum:

1*540 nm = d*sin(13.4°)

Solving for d, we get:

d = 1.22 μm

Now, for the second-order maximum:

2*540 nm = d*sin(θ)

Solving for θ, we get:

θ = sin^(-1)((2*540 nm)/d)

Plugging in d = 1.22 μm, we get:

θ = 28°

Therefore, the second-order maximum appears at an angle of 28°. Choice (D) is the correct answer.

A Wavelength of 540 Nm Yields a First-Order Maximum at 13.4°