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GRATINGS: Why Add More Slits?

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- Principal maxima become sharper
- Increases the contrast between the
- principal maxima and the subsidiary
- maxima

Rayleigh: principal maximum of one coincides with first minimum of the other

Interference minima when

From the condition

for interference maxima:

2001 Q2

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?

2001 Q13

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

Mirrors

Lenses

Compound systems

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.

Plane/flat

Concave

Convex

We assume light

goes from left

to right

object

at distance p

image

at distance q

erect/

upright

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.

Paraxial rays

principal axis

f = R/2

centre of curvature R