Physics 30 Lesson 12 Diffraction Gratings
Poisson’s bright spot
Thomas Young published the results from his double-slit experiment (Lesson 11) in 1807 which put the wave theory of light on a firm footing. However, so strong was Newton’s reputation and his corpuscular theory of light that Young’s results were not accepted until more than ten years later when, in 1819, Augustin Fresnel (1788–1827) presented to the French Academy a wave theory of light that predicted and explained interference and diffraction effects. (Refer to Pearson pages 691 to 692.)
Almost immediately after Fresnel introduced his wave theory, Simeon Poisson (1781–1840) pointed out what at first appeared as a counter-intuitive inference: that according to Fresnel's wave theory, if light from a point source were to fall on a solid disk, then light diffracted around the edges should constructively interfere at the center of the shadow. In other words, a bright spot should appear in the center of the shadow. That prediction seemed very unlikely. After attempting the experiment and failing to demonstrate the existence of a bright spot, Poisson claimed that he had refuted Fresnel’s theory.
But when the experiment was redone by Francois Arago in 1818, the bright spot was seen at the very center of the shadow! This was strong evidence for the wave theory and it was ironically referred to as Poisson’s Bright Spot. To the right is a photograph of the shadow cast by a coin using a (nearly) point source of light (a laser in this case). The bright spot is clearly visible at the center. Note that there are also bright and dark fringes beyond the shadow. These resemble the interference fringes of a double slit. Indeed, they are due to interference of waves diffracted around different parts of the disk, and the whole is referred to as a diffraction pattern.
A diffraction pattern exists around any sharp object illuminated by a point source, as shown in the photograph of a razor illuminated with laser light. We are not always aware of diffraction effects in our everyday life since most sources of light in everyday life are not point sources – so light from different parts of the source wash out the pattern.
A large number of equally spaced parallel slits is called a diffraction grating. (Refer to Pearson pages 692 to 694.) Gratings are often made by ruling very fine lines on glass with a diamond tip. The spaces in between the lines serve as slits. Gratings containing more than 10 000 slits per centimetre are common today. A double slit apparatus produces an interference pattern where the fringes tend to be broad and relatively undefined. Diffraction gratings produce very sharp and well defined bright fringes and dark fringes. Check out the video clip called P30 L12 Diffraction interference in D2L. The video shows how different colours (i.e. wavelengths) of light are diffracted by different amounts.
A similar derivation like the one demonstrated for the...