GRATINGS: Why Add More Slits?. Principal maxima become sharper Increases the contrast between the principal maxima and the subsidiary maxima. Dispersion of a diffraction grating. Resolving power of a diffraction grating.
Rayleigh: principal maximum of one coincides with first minimum of the other
Interference minima when
From the condition
for interference maxima:
a) Show that an ideal diffraction grating with narrow slits
spaced a distance d apart illuminated with light of
wavelength l will produce an intensity pattern with peaks at angles q given by
d sin (q) = n l,
where n is an integer.
b) If such a diffraction grating with 500 slits per mm is illuminated with 600 nm light, what is the maximum order of diffraction, n, that will be visible?
a) Describe the difference between the conditions under which Fraunhofer and Fresnel diffraction may be observed. Show that the intensity distribution in the Fraunhofer pattern of a slit of width w illuminated with light of wavelength l is
b) Describe Rayleigh's criterion for the resolution of images formed by a slit, and deduce from the above formula for the diffraction pattern that the minimum angular separation between two images which can just be resolved, at wavelength l, by a slit of width w, is l/w.
c) State how this expression is modified for a circular aperture of diameter D.
d) Use this result to calculate the smallest separation between two objects that can be resolved by a human eye with a pupil diameter of 2.5 mm at a distance of 250 mm, assuming a wavelength of 500 nm.
S&B: Chapter 36
Uses for above
Mirrors are used widely in optical instruments for
gathering light and forming images since they
work over a wider wavelength range and do not
have the problems of dispersion which are
associated with lenses and other refracting elements.
We assume light
goes from left
at distance p
at distance q
Images are located at the point from which
rays of light actually diverge or at the point
from which they appear to diverge.
A real image is formed when light rays pass
through and diverge from the image point.
A virtual image is formed when the light rays
do not pass through the image point but appear
to diverge from that point.
For plane mirrors:
The image is as far behind the mirror as the
object is in front of the mirror.
|p| = |q|
The image is unmagnified, virtual, and upright.
M = 1 (magnification)
The image has front-back reversal.
f = R/2
centre of curvature R