Evans SPH 4U1

Unit 5: Waves

Note 10: Diffraction Gratings

Reference: Chapter 10.3

Diffraction gratings are used to resolve light into spectra.  A diffraction grating consists of many closely spaced parallel slits.

The wave analysis of a diffraction grating pattern is like the analysis for double slit.  The waves passing through the slits interfere constructively (bright) when:

where m is the order of the bright line or maxima.

Diffraction gratings compared with typical double slit patterns:

~ There are many more slits giving more light energy and brighter interference patterns.

~ The maxima are much sharper and narrower.

~ The slits in a grating are closer together than slits in a double slit case so the separation between maxima is greater and the resolution is better.

~ Therefore using a diffraction grating is an accurate way to measure wavelength of light.

Crossed Gratings:

~ If you look through Vertical gratings to a point source of light you will see a horizontal diffraction pattern (figure 3a page 509 text)

~ Horizontal gratings will produce a vertical diffraction pattern (figure 3b page 509 text)

~ If you overlay a vertical grating and a horizontal grating on top of each other and look at a point source you will get a crossed-grating diffraction pattern (figure 3c page 509 text).

How a Spectroscope works:

If light striking a diffraction grating is made up of many different wavelengths (like white light), each wavelength will be diffracted at a different angle and each wavelength will make a pattern of bright maxima at different locations on the screen.

~ For white light there would be a white central maximum but the rest of the maxima would be a spectrum of colours - just like diffraction of white light into its colours through a prism. HOWEVER, as stated above, the pattern made by diffraction gratings are much more spread out and easier to see (than through a prism).  This is why diffraction gratings are used for spectral analysis (by a spectroscope).

~ In a spectroscope, light is directed through a 'collimator' (mirrors that make the source rays parallel). This parallel light is then passed through a diffraction grating . The angle can be measured accurately so the wavelength of light can be measured accurately.

Example:

At what angle will 575 nm yellow light produce a third-order maximum when passing through a grating of 800 lines /cm? (7.9 degrees)

Text Questions:

Page 509 #'s 1-4

Page 511 #'s 2-5