Gratings why add more slits
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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.

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Gratings why add more slits

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

Dispersion of a diffraction grating


Resolving power of a diffraction grating

Resolving power of a diffraction grating

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


Gratings why add more slits

Interference minima when


Gratings why add more slits

From the condition

for interference maxima:


Gratings why add more slits

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?


Gratings why add more slits

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.


Geometric optics

GEOMETRIC OPTICS

S&B: Chapter 36

Mirrors

Lenses

Compound systems

Uses for above


Mirrors

Mirrors

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


Plane flat mirrors

Plane/Flat Mirrors

object

at distance p

image

at distance q

erect/

upright


Virtual image

Virtual image


Gratings why add more slits

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.


Front back reversal

Front-back reversal


Gratings why add more slits

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.


Magnification lateral

Magnification (lateral)


Gratings why add more slits

Paraxial rays

principal axis

f = R/2

centre of curvature R


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