Question

Image a square aperture of width 149 \[Mu]m, 2775 mm away from a diffraction grating with a groove spacing of 1888 grooves/mm. You illuminate the diffraction grating by sending polychromatic light where the wavelengths are relatively close together and the average wavelength is 1037 nm through the square aperture onto the diffraction grating. What is the resolving power of the diffraction grating for second order light in this setup? (Assume the diffraction pattern is a Fraunhofer diffraction pattern.)

Answer 1

For mth diffraction order, the Resolving power is given by:

R = mN

where N = total number of slits/grooves illumination.

Here, there are 1888 x 1000 = 1888000 grooves per meter in a grating. So, number of grooves in 149 x 10 ^-6 m will be:

N = 1888000 x 149 x 10 ^-6 = 281.312 or approximately 281

these many grooves must be illuminated to capture the image of the square aperture.

for 2nd order, m = 2

therefore, R = (2)(281) = 562.

this is the resolving power for 2nd order light setup.