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Water waves at a barrier

Rayleigh waves at a flat/straight boundary

P

22incident22reflected

22incident = 22reflected

Circular wave

Flat boundary

Flat mirror image

An observer O, facing a mirror, observes a light source S. Wheredoes O perceive the mirror image of S to be located?

1. 12. 23. 34. 45. Some other location.6. The image of S cannot be

seen by O when O and S arelocated as shown.

Perception & Notation

What you see Whats out there How you draw it

Illusions

Virtual images & mirrors

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Parallel mirrors

Parallel mirrors

2 perpendicular mirrors

Perpendicular mirrors

So when light is reflected/transmitted,what direction exactly does it go?

It all depends on the angle and the material, ie. the new speed.

PFermats principle of least time Definition of straight: shortest distance between 2 points

Redefinition: path with shortest time between 2 points

The hurried ant problem on a box surface

Light travels in straight lines, but these include bendingones

These bends occur at media boundaries

Least time (pavement sand)

A group of sprinters gather at point P on a parking lot borderingabeach. They must run across the parking lot to a point Q onthe beach as quickly as possible. Which path from P to Q takesthe least time? You should consider the relative speeds of thesprinters on the hard surface of the parking lot and on loose sand..1. a 2. b 3. c 4. d 5. e 6. All paths take the same time.

Least time (sand pavement)

Suppose the sprinters wish to get from point Q on the beach topoint P on the parking lot as quickly as possible. Whichpath takes the least time?1. a 2. b 3. c 4. d 5. e 6. All paths take the same time.

Snells Snake Teams

v1 /v2 = sin 21/ sin22 = n2 / n1n1 = c / v1 & n2 = c / v2

Violet: more steps per minute (higher f requency)

Red: fewer steps per minute (lower frequency)

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Mirage

Fooled by curves...

< Densityeffectsdue to heat

Sunsets

After the fact...

< Density effectsdue to gravity

Sloping floors

Change of velocity via change of depth

Rayleigh water waves

Rayleigh water waves

Sloping floors & frequency

Frequency dependence of refraction

High frequency Low frequency

Frequencydependence

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Rearview mirrors

Day

Night

Undersea light seen from a helicopter

What would you see?

22critical

Top View

Seeing

What does the EYE detect?

< Color (frequency) 7 cone pixels< Brightness (amplitude)7 rod pixels< Angle (direction) 7 pixel locationNEITHER DETECTS historical NOR boundary informationDETECTS ONLY the light coming physically into the eye

What does the BRAIN do?< Fuses 2 images of the right & left eyes to get depth< Sorts patterns assuming unbent straight rays INTERPRETS data gathered IN the eye

INFERS (often mistakenly) historical & boundary information

Depth perception

It takes 2 eyes

Ice fishing

A fish swims below the surface of the water. Suppose an observeris looking at the fish from point Ostraight above the fish. Theobserver sees the fish at

1. a greater depth than it really is.2. the same depth.3. a smaller depth than it really is.

Depth of image in glass or water

Refraction at flat surface

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Viewing from above

Small angle approximation

Fishing from the bank

A fish swims below the surface of the water atP. An observer at O sees the fish at

1. a greater depth than it really is.2. the same depth.

3. a smaller depth than it really is.

Viewing at an angle (No small angle approx)

Serway/2ed Problem 25.42 A fish is at a depth d under water.Show that when viewed from an angle of incidence 2, theapparent depth of the fish is z=3dcos22 / sqrt(7+9cos222)

What is an image?

The recreation of a pattern....

An optical image

Is made by bending light* in order to reorganize it

PThat means using Mirrors Lenses

Holes

Edges

(This excludes tracking phase as is the case with holograms, which alsoreorganize light without bending it)

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Lens focal length

Lenses as sets of prisms

Point source vs. Source at 4

Using the focal length to transform one into the other

Mirror focal point

Set of flat surfaces