What resolving power must a diffraction grating have in order to distinguish wavelengths of 686.30 nm and 687.50 nm? (1 nm = 10−⁹ m) A)343 B)572 C)686.9 D)915 E)687.5

Question

Quizplus · Accepted Answer

The formula for the resolving power of a diffraction grating is given by:

R = N * dλ / D

where R is the resolving power, N is the number of lines in the grating, d is the spacing between adjacent lines, λ is the wavelength of the light, and D is the diameter of the aperture.

We are given the two wavelengths:

λ1 = 686.30 nm

λ2 = 687.50 nm

To distinguish these two wavelengths, we need the resolving power to be such that:

R = λ2 - λ1 = 1.20 nm

We can rearrange the formula to solve for d:

d = R * D / N * λ

We can assume a reasonable value for the diameter of the aperture, say D = 1 cm = 0.01 m. We can also assume a reasonable number of lines for a diffraction grating, say N = 10^5.

Substituting these values along with the values of R and λ, we get:

d = 572 nm

Therefore, the resolving power must be 572 in order to distinguish wavelengths of 686.30 nm and 687.50 nm.

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