Question

A diffraction grating has a grating spacing of d=1234 nm. It is used with light of wavelength 555 nm. At what angle (in degrees) will the first-order diffraction image be seen?

Answer 1

The angle at which the first-order diffraction image is seen can be found using the formula sin(θ) = mλ/d, where θ is the angle of diffraction, m is the order of the maximum, λ is the wavelength of light, and d is the grating spacing. In this case, the angle is approximately 0.450°.

Step-by-step explanation:

To find the angle at which the first-order diffraction image is seen, we can use the formula for calculating the angle of diffraction for a diffraction grating:

sin(θ) = mλ/d

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

In this case, we have a grating spacing of d = 1234 nm and light of wavelength λ = 555 nm. We are interested in the first-order maximum (m = 1). Plugging in these values into the formula:

sin(θ) = (1)(555 nm) / (1234 nm)

θ ≈ 0.450°

Therefore, the first-order diffraction image will be seen at an angle of approximately 0.450°.