Physics 116 Session 27 Diffraction gratings Postulates of - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Session 27

Diffraction gratings Postulates of Relativity

Nov 14, 2011

• HW 5 due today!

Announcements

3

Lecture Schedule

(up to exam 3)

Today

Diffraction for a circular aperture: resolution

• Pinholes also show diffraction fringes

– Similar to single slit pattern, but with circular symmetry – Mathematical form is called the Airy function – Angle to first dark fringe for a pinhole is

• Rayleigh Criterion: resolution for aperture of diameter D

(a): One pinhole (b): Two, just separable (c): Two, not separable! – Can just resolve 2 pinholes if their 1st minima overlap:

Telescope, camera, binoculars and human eye = circular apertures ! Rayleigh criterion lets us estimate resolution limits for optical devices Last time:

• Light with wavelength 676 nm strikes a single slit of width 7.64 microns, and

goes to a screen 185 cm away. What is distance in cm of 1st bright fringe above the central fringe? First bright fringe is about halfway between dark fringes for m=1 and m=2 We can find its angle by using “m=1.5” in the dark-fringe formula:

• A spy satellite orbits at 160 km altitude. What camera lens diameter is needed

to resolve objects of size 30 cm (meaning: distinguish two objects a foot apart)?

5

Examples

(same as finding location of dark fringes 1 and 2, and then finding their midpoint) Tangent of angle = y/L:

y

L Assuming light wavelength 550 nm: (~ center of human vision range)

2-slits revisited

diffraction pattern due to each slit Interference pattern for 2 slits

w a w ! w=0.25mm, a=0.9mm, "=632nm

• Now that we know about diffraction, we can understand details of 2-slit

interference patterns

• Each slit’s diffraction pattern modulates the 2-slit interference pattern

Result:

From 2 to N slits: diffraction gratings

• For N>>2 slits, uniformly spaced, we get an interference pattern that has

– Many sharply defined bright fringes, equally spaced (principal maxima)

• Approximately same intensity for all
• Increasing N sharpens the principal maxima

– In between, many very dim secondary fringes (secondary maxima)

• For very large N, slit mask = “diffraction grating”

– for m=0 all wavelengths have max at q=0 – for m>0, maxima at ! " : can use grating as a spectroscope

For w=0.25mm, a=0.5mm, "=632nm: N=4 N=8

8

Diffraction gratings

• N-slit interference produces pattern with fringe spacings

dependent on wavelength

• Diffraction grating = thousands of closely spaced slits

– Very sharp fringes build up for each color, with contributions from all slits – Better than a prism (no light absorption in glass) – Can use mirror surface with fine-line pattern also: reflection grating

Rainbow effect looking at white light reflected in a CD Diffraction grating with red + blue wavelengths incident: colors are separated due to different angles for their maxima

• A laser emits 2 wavelengths, 420nm and 630nm. At what angle and for what order

will maxima for both wavelengths coincide, for a grating with N=450 lines/mm? We want same angle to be order number m for one line, and n for the other; both must be integers: Try n=1, 2… and find first value of n that gives integer m n= 2 gives m=3: so find angle in degrees by putting in m=3 above

9

Examples

d sinm = m1 d sinn = n2 spacing d (in mm) = 1/ N lines / mm

( )

m = sin1 m1 d = sin1 m1N

( )

450 lines / mm = 450 106 lines / nm = sin1 m 420 nm

( ) 450 106 nm1

( )

• = sin1 m 0.189

( )

• n = sin1 n 630 nm

( ) 450 106 nm1

( )

• = sin1 n 0.2835

( )

• so we want m 0.189

( ) = n 0.2835 ( )

• m = n 0.2835

0.189

• = 1.5n

n = -2 -1 0 +1 +2 m = -3 -2 -1 0 +1 +2 +3

typos corrected:

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“Modern” physics

• Next set of topics: a brief introduction to relativity and quantum

theory, atomic and nuclear physics

– Modern physics (term coined in mid-20th century!) – As opposed to: “classical physics” (Newton and Maxwell), where

• Time ticks on, independent of physical objects or their motions
• EM radiation consists of waves, not particles
• With fully detailed info on its physical state now, motion of a

body can be predicted precisely, into the future

• In 1895, physics was thought to be “almost finished”

– Just a few little problems remained to be settled… (sound familiar?)

• 1. How to tweak Maxwell’s equations to make them obey Galilean Relativity?
• 2. Why do atoms emit light only at specific wavelengths (“line spectra”)
• 3. Explanations for a few peculiar experimental results:

“Blackbody radiation” (thermal emission of EM waves) spectrum “Photoelectric effect” (emission of charge when light hits metal surfaces)

First, item 1 above: relativity

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Review: Galileo’s “common sense” relativity (c. 1600)

• Example: Bill and Phil are (at first) both standing still

– Bill fires a gun: bullet’s speed is 1000 m/s relative to gun

• Both agree: bullet speed is 1000 m/s

– Next, Phil rides on train with speed 100 m/s, shoots gun forward

• Phil says v=1000 m/s, but Bill says it is 1100 m/s
• Both are right: describing motion in their reference frames

– Bill agrees he would say 1000 m/s if he were on train – Phil agrees he would say 1100 m/s if he were on ground – Both agree bullet “really” moves 1100 m/s (Earth reference) First: Both are at rest Next: Phil rides on 100 m/s train moving past Bill Q: what if Phil fired backward ?

1000 m/s 1000 m/s 100 m/s Earth Earth

Train B P B P

12

Oops: A little problem with Maxwell’s equations

• By 1880s, Maxwell’s work was in everyday technology

– Every generator, motor, telegraph, telephone proved him right

• Just like quantum theory today…computer chips, lasers
• Problem: Maxwell equations don’t obey Galilean relativity !

– Simple example: imagine Phil holds an electric charge

• Both standing still: both see only electric field of charge
• Phil is on moving train, Bill remains at rest:

– Bill sees moving charge = current magnetic field B – Phil still sees only electric field E of static charge First: Both are at rest Both see E field and no B field Next: Phil rides on 100 m/s train moving past Bill Phil sees only E field, but Bill sees a B field

100 m/s Earth Earth

Train B B P

+

P

+ Moving charge = current I

Static charge