•Principal maxima become sharper

•Increases the contrast between the principal maxima and the subsidiarymaxima

GRATINGS: Why Add More Slits?

Instrumental broadening

2 for 0m

Nd

Dispersion of a diffraction gratingDispersion of a diffraction grating

sin

cos d d

dd cos m

d m

d m

md

For small :

d md d

Resolving power Resolving power of a diffraction gratingof a diffraction grating

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

min

R

Interference minima when

sin0

sin

2 ( 1) ( 1), , , , ,

N

N NN N N N

2

0 2

For -slit interference

sin where sin

sin

N

NI I d

sindN

sindN

2 2sin

2

dN

N

2 2cos dd

N

2 2cos dd

N

sin

cos d d

d m

d m

From the conditionfor interference maxima:

2 2dm

N

Nm R

2001 Q22001 Q2

a) Show that an ideal diffraction grating with narrow slitsa) Show that an ideal diffraction grating with narrow slitsspaced a distance spaced a distance dd apart illuminated with light of apart illuminated with light ofwavelength wavelength will produce an intensity pattern with peaks at will produce an intensity pattern with peaks at angles angles given by given by

dd sin ( sin () = n ) = n ,,

where where nn is an integer. is an integer.

b) If such a diffraction grating with 500 slits per mm is b) If such a diffraction grating with 500 slits per mm is illuminated with 600 nm light, what is the maximum order of illuminated with 600 nm light, what is the maximum order of diffraction, diffraction, nn, that will be visible?, that will be visible?

2001 Q132001 Q13

a) Describe the difference between the conditions under which Fraunhofer a) Describe the difference between the conditions under which Fraunhofer and Fresnel diffraction may be observed. Show that the intensity distribution and Fresnel diffraction may be observed. Show that the intensity distribution in the Fraunhofer pattern of a slit of width in the Fraunhofer pattern of a slit of width ww illuminated with light of illuminated with light of wavelength wavelength is is

b) Describe Rayleigh's criterion for the resolution of images formed by a slit, 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 and deduce from the above formula for the diffraction pattern that the minimum angular separation between two images which can just be minimum angular separation between two images which can just be resolved, at wavelength resolved, at wavelength , by a slit of width , by a slit of width ww, is , is //ww..

c) State how this expression is modified for a circular aperture of diameter c) State how this expression is modified for a circular aperture of diameter DD..

d) Use this result to calculate the smallest separation between two objects 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 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.distance of 250 mm, assuming a wavelength of 500 nm.

2sin

( ) (0) where sinw

I I

optics

mirrors lenses

Compound/ thick lenses

Lens-makers’ eq’n

Ref raction at spherical

surf ace

Plane/ convex/ concave

Thin lenses

Real/ Virtual images

systems

aberrations

Camera/ eye/magnifier/

microscope/ telescope

Ray tracing

GEOMETRIC OPTICSGEOMETRIC OPTICS

S&B: Chapter 36

MirrorsLenses

Compound systemsUses for above

MirrorsMirrors

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 lightgoes from leftto right

i r

Plane/Flat MirrorsPlane/Flat Mirrors

object image

erect/upright

at distance p at distance q

Virtual imageVirtual image

Images are located at the point from whichrays of light actually diverge or at the pointfrom which they appear to diverge.

A real image is formed when light rays passthrough and diverge from the image point.

A virtual image is formed when the light rays do not pass through the image point but appearto diverge from that point.

Front-back reversalFront-back reversal

The image is as far behind the mirror as theobject is in front of the mirror. |p| = |q|

The image is unmagnified, virtual, and upright. M = 1 (magnification)

The image has front-back reversal.

For plane mirrors:

Magnification (lateral)Magnification (lateral)height of imageheight of object

1 (for plane mirror)

image distanceobject distance

M

M

qM

p

Paraxial rays

f = R/2

principal axis

centre of curvature R