A 17-mm-wide grating has rulings of 530 lines per millimeter.White light is incident normally on the grating.What is the longest wavelength that forms an intensity maximum in the fifth order?

Question

Quizplus · Accepted Answer

The longest wavelength that forms an intensity maximum in the fifth order is given by:$$\lambda = \frac{d \sin 	heta}{m}$$where d is the grating spacing, θ is the angle of diffraction, and m is the order of the maximum.For normal incidence, θ = 0, so:$$\lambda = \frac{d}{m}$$Substituting the given values, we get:$$\lambda = \frac{17 	ext{ mm} 	imes 10^{-3} 	ext{ m/mm}}{5} = 3.4 	imes 10^{-6} 	ext{ m} = 3400 	ext{ nm}$$This is the longest wavelength that forms an intensity maximum in any order.

A 17-Mm-Wide Grating Has Rulings of 530 Lines Per Millimeter