Agenda

Agenda

• Monday– Diffraction – Problems– How small?– How many?

• Tuesday– Diffraction – Laboratory, Quiz on Interference

• Wed– Review

• Fri – Bonus Quiz

Basic Diffraction Formula

• x = m (constructive)

• x = (m+1/2) (constructive)– m integer

• Open question– What is x?

Multiple Slits

• x = m (constructive)

• x = (m+1/2) (constructive)– m integer

• Open question– x = dsin

Equation vs. Experiment

Coherent, monochromatic Lightwavelength

Slits (Turned perp.)Rectangular

Screen

m

3

2

1

0

-1

-2

-3

dsin() = m

d

Examine Situation for Given LaserMeans: fixed

Coherent, monochromatic Lightwavelength

Slits (Turned perp.)

Screen

m

3

2

1

0

-1

-2

-3

dsin() = m

d

Range of possible d values?Given: fixed

Coherent, monochromatic Lightwavelength

Slits (Turned perp.)

Screen

m

3

2

1

0

-1

-2

-3

dsin() = m

d

Range of possible d values?Given: fixed

dsin() = m d = m / sin()

Anything related to range of d?Try big & small….

Range of possible d values?Given: fixed

dsin() = m d = m / sin()

How big can d be?Pretty big, m can range to infinity….If d is big, what happens to angle?sin() = m/d….Large slit spacing, all diffraction squeezed togetherInterference exists – just all overlaps – beam behavior

Large Distance(Assume large width…)

Coherent, monochromatic Lightwavelength

Slits (Turned perp.)

Screen

d

dsin() = m

Slit one

Slit Two

Range of possible d values?Given: fixed

dsin() = m d = m / sin() How small can d be?

Pretty small, m can be zeroHow about for anything but m = 0Smallest m =1d = /sin()d small when sin() big, sin() <= 1smallest d for m=1 diffraction: d = Replace: sin()=msin() = mimplies if d = , three diffraction spotsif d < , no diffraction (m=0?)

Range of possible d values?Given: fixed

Coherent, monochromatic Lightwavelength

Slits (Turned perp.)

Screen

m

1

0

-1dsin() = m

d ~

What Happens?

• Diffraction from spacing & width– Overlaying patterns, superposition

• 3 slits, all same spacing– Very similar to two slits

• Tons of slits, all same spacing– Refined interference. Focused maxima

• Move screen farther away from slits– Bigger angle/distance on screen

• Move light source, leave rest same– Nothing

ResolutionWhen can you identify 2 objects?

Coherent, monochromatic Lightwavelength

Slits (Turned perp.)

Screen

m

1

0

-1dsin() = m

d ~ w ~

Not Here…

ResolutionWhen can you identify 2 objects?

Begin with diffraction

Diffraction of light through a circular aperture1st ring (spot) sin() = 1.22/D Same setup idea as before

ResolutionWhen can you identify 2 objects?

Begin with diffraction

Diffraction of light around a circular block1st ring (spot) sin() = 1.22/D Same setup idea as before

Things that might cause diffraction rings…Pits/dust on glassesIris of your eyeTelescope LensRaindrops

Pretty Picture

Moon

Raindrop

What you see

Headlights

Resolved (barely) Unresolved

Issue

• How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work)

• sin() = 1.22/D

1.5 m

Small Angle sin() ~ tan() ~ [radians]

Issue

• How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work)

• = 1.22/D • = y/L• What is D?

1.5 m = y

Small Angle sin() ~ tan() ~ [radians]

L

Issue

• How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work)

• = 1.22/D • = y/L• pupil: D ~ 5 mm • What is ?

1.5 m = y

Small Angle sin() ~ tan() ~ [radians]

L

Issue• How close must a car be before you can tell it is NOT a motorcycle.

(assume both headlights work)• = 1.22/D • = y/L• pupil: D ~ 5 mm

• GREEN ~ 500 nm

• Calculation Time

1.5 m = y

Small Angle sin() ~ tan() ~ [radians]

L

Issue• How close must a car be before you can tell it is NOT a motorcycle.

(assume both headlights work)• = 1.22/D • = y/L• y/L = 1.22/D• L/y = D/(1.22)

1.5 m = y

Small Angle sin() ~ tan() ~ [radians]

L

= 500 nm

D = 5 mm

Issue• How close must a car be before you can tell it is NOT a motorcycle.

(assume both headlights work)• = 1.22/D • L/y = D/(1.22)• L = Dy/(1.22) = 12km ~ 7 miles• Little far, but not crazy far• aberrations blur image more here

1.5 m = y

Small Angle sin() ~ tan() ~ [radians]

L

= 500 nm

D = 5 mm

Agenda

• Monday– Diffraction – Problems

• Tuesday– Diffraction – Laboratory, Quiz on Interference

• Wed– Review

• Fri – Bonus Quiz