Light of the same wavelength passes through two diffraction gratings.One grating has 4000 lines/cm,and the other one has 6000 lines/cm.Which grating will spread the light through a larger angle in the first-order pattern?
A)the 4000-line grating
B)the 6000-line grating
C)Both gratings spread the light the same.

Question

Quizplus · Accepted Answer

The angle of diffraction is given by the equation θ = sin⁻¹(mλ/d), where m is the order of diffraction, λ is the wavelength, and d is the distance between adjacent slits on the grating. Since the wavelength and the distance between slits are the same for both gratings, the angle of diffraction depends only on the order of diffraction and the number of lines per unit length on the grating. For the first-order pattern, m = 1, and the angle of diffraction is proportional to 1/d. Therefore, the grating with a higher density of lines (6000 lines/cm) will spread the light through a larger angle than the grating with a lower density of lines (4000 lines/cm).

Light of the Same Wavelength Passes Through Two Diffraction Gratings