4 Apr 2002 Physics 102 Lecture 7 1

The Wave Nature of Light

Physics 102

Lecture 7

4 April 2002

Pick up Grating & Foil & Pin

4 Apr 2002 Physics 102 Lecture 7 2

� Last week we saw that light travels from place to placealong “rays” that trace paths as particles would.

Geometric optics:

� However, light also produces interference patterns justlike sound or water waves.

Wave optics:

� Young (as in Young’s Modulus) demonstrated interferenceof light in 1801 using a “double slit” apparatus.

Light acts like a wave!

4 Apr 2002 Physics 102 Lecture 7 3

Two slit interference

� Consider light passing through two slits in a screen:

� constructive (bright) fringes:� destructive (dark) sin d, , , ,

sin

θ λθ λ

== ==== ++(( ))

m m

m d

0 1 212

K

Constructive interference

4 Apr 2002 Physics 102 Lecture 7 4

Single slit diffraction

Maximum

m=1 min

m=2 min

wm

2 2sinθ λ==

θ

Interference occurs with a single slit!

Each point on the wave front acts as anew source of secondary sphericalwaves: Huygens’ construction

A bright spot always appears at thecenter.

These rays correspond toa dark fringe.

4 Apr 2002 Physics 102 Lecture 7 5

A single slit diffraction patternis formed with a slit of width w.

The width of the slit is then doubled.Considering the central portion of thediffraction pattern....

A. The angular size of the central diffraction spot doubles.

B. The angular size of the pattern is reduced by two.

C. The central spot stays the same size but the minima movecloser to the central spot.

D. More light gets through so the pattern looks the same but isbrighter.

4 Apr 2002 Physics 102 Lecture 7 6

1 slit

2 slits

3 slits

4 slits

5 slits

4 Apr 2002 Physics 102 Lecture 7 7

Multislit interference (gratings)

� With multiple slits, the maxima occur only whenconstructive interference occurs from all the grating slits.

� Thus, the centers of lines are at the same places aswith two slits

but now the lines are much narrower and brighter. Wecall this a diffraction grating.

� The pattern from a single slit is still imposed on themultislit pattern.

,...2,1,0,sin == mdmλθ

4 Apr 2002 Physics 102 Lecture 7 8

Interference from CDs

CD

For maxima

m=1

4 Apr 2002 Physics 102 Lecture 7 9

A green laser (wavelength=500 nm) isreflected off a plate that contains smallfeatures.

Spots are observed on a wall 10 m away.

What is the approximate separation, D, ofthe features on the plate ?

A. Not enough information to tell.

B. D = 15 nanometers

C. D = 15 micrometers

D. D = 15 millimeters

4 Apr 2002 Physics 102 Lecture 7 10

X-Ray Diffraction

� X-rays are electromagnetic radiation, like light,but with a wavelength of order 0.5x10-10 m(atomic radius)

� A crystal in an X-ray beam acts like a diffractiongrating, producing “Laue patterns” or “Braggpeaks”

� Studying these patterns reveals the crystallinestructure

� The structure of DNA was determined by Watsonand Crick using X-ray diffraction.

4 Apr 2002 Physics 102 Lecture 7 11

A diffraction grating is illuminated with red light atnormal incidence. The pattern seen on a screen behindthe grating consists of three red spots, one at zerodegrees (straight through) and one each at ±45°. Younow add green light of equal intensity, coming in thesame direction as the red light. The new patternconsists of:

A. Red spots at 0° and ±45°.B. Green spots at 0° and ±45°.C. Yellow spots at 0° and ±45°.D. A yellow spot at 0°, red spots at ±45°, and green spots slightly farther out.E. A yellow spot at 0°, red spots at ±45°, and green spots slightly closer in.

From Eric Mazur

4 Apr 2002 Physics 102 Lecture 7 12

Spectrum of Hg

300 400 500 nm

With a grating, we can study the spectra of atoms.

Emission

lines from

Hg

Look to the right!

4 Apr 2002 Physics 102 Lecture 7 13

From Eric Mazur

Imagine holding a circular disk in a beam of monochromatic light. If diffraction occurs at the edge of the disk, the center of the shadow of the disk is:

A. A bright spot.B. Darker than the rest of the shadow.C. Bright are dark, depending on the distance to the screen.D. As dark as the rest of the shadow, but not as dark as withoutdiffraction.

4 Apr 2002 Physics 102 Lecture 7 14

Shadow of a ball bearing in laser light

4 Apr 2002 Physics 102 Lecture 7 15

The Rayleigh Criterion� Two point objects (e.g., headlights) can just be resolved

if the first dark fringe in the diffraction pattern of onefalls directly on the bright central fringe of the other.

� If the angle is small, then (NB: the angle must be expressed in radians)

� For the eye, D=2.5 mm, and red light,

~ 0.0002~0.01 deg.

This is equivalent to 2 mm at 10 m distance

sin . /θ θ λmin min≈ = 1 22 D

4 Apr 2002 Physics 102 Lecture 7 16

Interference in thin films

� Light reflecting off two layersof a surface can interfere withitself con/destructively.

� Light undergoes a halfwavelength phase changewhen reflecting from a moreoptically dense medium.

� Constructive interference:

,...2,1,0,2 filmfilm21 ==+ mmt λλ

film

4 Apr 2002 Physics 102 Lecture 7 17

Newton’s rings

Here a lens projects the diverging rays onto the wall

4 Apr 2002 Physics 102 Lecture 7 18

Soap film—wedge interference

Slightly divergingrays require aconverging lens toproject on the wall.

Lens inverts image.

Gravity draws filmapproximately intoa wedge.

Puzzler: What would the film look like in transmitted light?

What happens to the reflected light when the film gets very thin?