Lesson: Resolution of Wave Sources Physics • 9th Grade

In this lesson, we will learn how to define the resolution of objects and relate their separations to gap widths that waves from the objects pass through.

Lesson Plan

Students will be able to

recall that the Rayleigh criterion for the spatial resolution of sources of waves defines just resolvable sources as those for which the waves from both sources are diffracted by passing through the same aperture and that the position of the central maximum of the intensity pattern of the waves of one of the sources is at the position of the first order minimum of the intensity pattern of the waves of the other source,
apply the equation , where is the angular distance between two just resolvable sources of waves of wavelength that are separated by a distance and whose waves both pass through an aperture that is effectively one dimensional,
apply the equation , where is the angular distance between two just resolvable sources of waves of wavelength that are separated by a distance and whose waves both pass through an aperture that is circular.

Lesson Worksheet

Q1:

Two light sources emit light that passes through a narrow slit 1.89 μm wide. The angle between lines from each of the light sources that intersect at the center of the slit is 0.265 rad. What wavelength of light must the sources emit to be just resolvable according to the Rayleigh criterion from the diffraction patterns that they produce?

Q2:

Two light sources emit light with a wavelength of 545 nm that passes through a narrow slit that is 4.33 μm wide. The light sources are just resolvable according to the Rayleigh criterion from the diffraction patterns produced. What is the angle between lines from each of the light sources that intersect at the center of the slit?

Q3:

Two light sources emit 555 nm wavelength light that passes through a circular opening. The light sources are just resolvable according to the Rayleigh criterion from the diffraction patterns they produce. The angle between the lines from each of the light sources that intersect at the center of the opening is 0.221 rad. What is the diameter of the opening?