Question

Wave Model of EMR - Compare the similarities and differences of the patterns produced by the dispersion of white light through a prism and the interference pattern produced by a diffraction grating.

Answer 1

Solution

Similarities

1. Both of them transform the white light into its component colours(or wavelengths)
2. A continuous spectrum is obtained if the incident white light contains all the wavelengths (like the sunlight)
3. A discrete spectrum is obtained if the incident light contains only certain wavelengths (like a atomic de excitation radiation)
4. The despersive power (extent of angular separation that can be produced) by varying prism/grating properties.

Differences

Dispersion through prism	Diffraction through grating
It utilizes the property of dispersive nature of prism material. Each wavelength possess different speed as it pass through prism material. This property combined with special geometry of prism is used to separate them out	It utilizes interference effect of electromagnetic waves. The diffraction grating causes constructive interference of certain wavelengths occure at certain regions and destructive interference of all other wavelengths.
No white light will be visible after dispersion through prism	Constructive interference of all wavelengths occure at the central maximum point and hence white light can be observed even after light passing through the grating at the central Maxima region.
No higher order spectra.	Higher order (second order, m=2) spectra can be observed at farther angular regions. Also the diffraction patterns are observable to left and right of central Maxima region.
The dispersive power of prism is, Where mu2 and mu1 are refractive index of violet and red wavelengths in the prism material. And mu is the mean of those.	Dispersive power of grating is, Where N is the number of lines per unit length of grating. n is the order of spectrum and theta is the angle of diffraction Maxima from central Maxima.