Lecture 15Ray Optics Chapter 23

PHYSICS 270Dennis Papadopoulos

March 9, 2010

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θ =sin−1(λ /a)

Wave vs. Ray Model

≈ nm

Ray Optics

Line of sight

Self Luminous vs. Reflected

Important Concepts

Pictorial Representation - Ray Diagrams

Apertures – Camera Obscura

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hi /ho = di /do

A long, thin light bulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

A long, thin light bulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

Light spreads horizontally due to different parts of the lightbulb

Light spreads vertically as it goes through the vertical aperture

The Plane Mirror – Virtual Image

Reflected rays coming from point P’ – The Virtual; Image Point – s=s’

Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors?

A. 1

B. 2

C. 3

D. 4

A. 1

B. 2

C. 3

D. 4

Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors?

Image FormationObject point (P,Q) maps to Virtual Image point (P’,Q’) : Rule

Index of Refraction

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fλ = v

v = c /n

Phase of wave rotates faster in materials than in

vacuum

Reflection and Refraction

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θi =θ r

Ptolemy 140 AD

Snell 1621sinθin sinθr

Snell’s law allow us to predict how light is going to bend in going fro air to water n=1.5

Is there a way of thinking that makes this evident and proves its generality -> Fermat

Fermat’s Principle of Least Time

Of all possible paths that light takes to get from one point to another light takes the path that corresponds to the shortest time

AEB=AEB’ Shortest length from A to B

after hitting the mirror is the one that goes as a straight line from A to B’, i.e. ACB’.Notice that ACB has equal incidence and reflection

angles

Angle BCF=Angle B’CF= Angle DCA

Fermat’s Principle for Refraction

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v = c /n

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v sinθ i = c sinθ rsinθ i = n sinθ r

Snell’s law

θ

θr

The slower the medium the smaller the refraction angle