The Geometry of Interference and Diffraction SPH4U

Two Point Source Interference Consider the interference pattern for two point sources in phase (e.g., two slits). nodal line constructive interference

In Phase Along the line halfway between the two slits, the waves will be in phase because the path length is the same. A bright spot would appear on the screen.

In Phase Along the line halfway between the two slits, the waves will be in phase because the path length is the same. A bright spot would appear on the screen. This bright spot is called the central maximum.

Out of Phase A little to the side of the central maximum (at an angle q), the path difference between the waves is ½l, and the waves will arrive out of phase, creating a dark spot.

In Phase A little bit further to the side and the path difference is l. The waves will be in phase again, creating another bright spot.

The Dark Spots Let’s find the position of each of the dark spots, where the path difference is (n – ½)l.

The Dark Spots n = # of dark spots from the central maximum d = separation between slits L = distance to the screen xn = distance between dark spot and central maximum

The Dark Spots

The Dark Spots

The Dark Spots

Example Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

Example Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

Example Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

Example Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

The Bright Spots Similarly, for bright spots away from the central maximum:

Diffraction Gratings A diffraction grating has a large number of equally spaced slits and a similar interference pattern. The primary difference between the patterns is that the maxima are much brighter and sharper.

Diffraction Gratings The locations of the maxima are still given by

Single Slit Diffraction Diffraction through a single slit may be analyzed similarly.

Huygen’s Principle Consider each of the points along the slit as a point source of wavelets. The wavelets will all be in phase at the central maximum.

Out of Phase At some angle q, there is a l path difference between the top and bottom of the slit. Each point therefore has a l/2 (out of phase) partner: 1 and 7, 2 and 8, etc., resulting in destructive interference.

Out of Phase At some angle q, there is a l path difference between the top and bottom of the slit. Each point therefore has a l/2 (out of phase) partner: 1 and 7, 2 and 8, etc., resulting in destructive interference. y just to help differentiate the equations

Similarly Secondary maximum Second dark spot

Minima The minima occur at

Example Monochromatic light of wavelength 670 nm passes through a slit width of 12 mm. A screen is placed 0.30 m away. What is the width of the central maximum?

Example Monochromatic light of wavelength 670 nm passes through a slit width of 12 mm. A screen is placed 0.30 m away. What is the width of the central maximum?

Example Monochromatic light of wavelength 670 nm passes through a slit width of 12 mm. A screen is placed 0.30 m away. What is the width of the central maximum?

Resolution Resolution is the ability of an instrument to separate the images of two objects.

Resolution The smaller the aperture, the greater the diffraction and the lower the resolution.

More Practice Textbook Questions p. 473 #2, 5, 6 p. 504 #2, 4, 5 Tomorrow: Interference of Light Lab