Monochromatic light is normally incident on a diffraction grating that is 1 cm wide and has 10,000 slits. The first order line is deviated at a 30$\degree$ angle. What is the wavelength, in nm, of the incident light?
A) 300
B) 400
C) 500
D) 600
E) 1000

Question

Quizplus · Accepted Answer

The formula for calculating the wavelength of light based on the diffraction grating is:

λ = d * sin(θ)
where
d = distance between adjacent slits (given by width of the grating divided by the number of slits)
θ = angle of deviation of the first order line

Plugging in the values given:
d = 1 cm / 10,000 = 0.0001 cm
θ = 30 degrees

Converting units:
d = 0.000001 m
θ = 0.5236 radians

Plugging these values into the formula gives:

λ = 0.000001 * sin(0.5236) = 0.000000548 m = 548 nm

Therefore, the wavelength of light is 548 nm, which corresponds to Choice C.

Monochromatic Light Is Normally Incident on a Diffraction Grating That °\degree°

Monochromatic Light Is Normally Incident on a Diffraction Grating That $\degree$