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Geometrical 3.1 and In are • Geometrical Optics considered to move in straight lines. • Reflection This is a good description as long as the • Refraction waves do not pass through small openings • Total Internal Refraction (compared to λ) •

Christian Huygens

Light waves Rays are perpendicularWave front to fronts

to wave fronts

Rays are not physical entities but are a convenient representation of a light wave.

(surfaces with constant phase - e.g. maxima)

Specular reflection Reflection Rough surface Flat surface Light reflected in all directions Light reflected in one direction • Two general types of reflection – – Diffuse reflection • Most of geometric optics deals with specular reflection. • However, most of the time ambient lighting is due to diffuse reflection.

1 Transmission and Reflection at an What are some examples of these processes in this interface picture.

Reflection Transmission Specular Reflection Absorption x Incident wave Diffuse reflection ()

medium 1 medium 2 Transmission

Absorption

Law of Reflection Full length The angle of reflection equals the angle of incidence A 6 ft tall man wants to install a mirror tall enough to see his ' whole body. How tall a mirror is needed? θ=θ11

h1 ½h1

½h2 h2

Angle of incidence Angle of reflection

Reflecting surface hmirror = ½ (h1 + h2) = ½ (6) =3 ft

Multiple reflections 2-Dimensional Corner reflector

Mirror 2 2 perpendicular reflect • For multiple reflections use the law of a light beam in a perpendicular to both mirrors back along the opposite direction reflection for each reflecting surface. θ2 θ2

θ1

θ1 we want to show that Mirror 1 o θ21=−90 θ

90-θ1 o θ1 +θ2 = 90

2 Corner reflectors on the moon used to measure the distance to the earth by Refraction measuring the round trip time of light. • Refraction is the bending of light when it passes across an interface between two materials. • Due to the differences in the in different media.

Speed of light in a medium Transmission across an interface Excites oscillation of electrons in medium The speed of the wave Wave in vacuum changes. The frequency remains the same. The changes c→ v→

Superposition of waves leads to slower speed in the medium v , compared to the speed of light in vacuum. c. c Index of refraction n = v

Refraction and Reflection

The light beam (3) is refracted at the interface.

3 Snell’s Law of Refraction Going from to air n1122 sinθ= n sin θ n sinθ =θ n sin Going from air to glass 1122 n2 < n1

θ2 > θ1

n2 > n1

θ2 < θ1

(sinθ increases with θ )

Example 22.2 Example 22.4

Find the angle of refraction for Show that light going through an angle of incidence of 30o in a flat slab is not deviated in going from air to glass angle.

(nglass =1.52) First interface

n1122 sinθ= n sin θ n1122 sinθ =θ n sin

nsinθ 1.00(sin30) Second interface sinθ= 11==0.33 2 1.52 n2 angle of incidence = θ2 o nsin2233θ =θ nsin θ=2 arcsin(0.33) = 19.3

then nsin1133θ =θ nsin Angle is the same but beam displaced since n1 =n3 θ1 = θ3

Huygen’s Principle Huygen’s Picture of a Plane wave

• All points in a given wave front are taken as point sources for the production of spherical secondary wavelets which propagate in space. After some time the new wave front is the tangent to the wavelets.

4 Huygen’s Picture of a Spherical Huygen’s Explanation of Reflection wave

therefore two sides and an angle equal θincidence = θreflection ∴ similar triangles

θ1 = θ’1

Huygen’s explanation for Refraction

Lsinθ1 = v1t

Lsinθ2 = v2t L sinθ v • 1 = 1 sinθ2 v2 new wave front 11 sinθ12=θ sin vv12

n1 sinθ1 =n2 sinθ2

Fig. 22-24b, p.741

Total Internal Reflection Total Internal Reflection

When the angle of refraction equals or exceeds 90o

All the light is internally reflected

5 -Light Pipe Fiber Optics An optical fiber (light pipe) confines the light inside the material by total internal reflection. If the Fiber optics are used of the fiber is 1.52 what is the smallest angle of incidence extensively in possible when the light pipe is in air. communications. n =1.00 Telephone, Internet, θ2 = 90 2

θ n =1.52 The high frequency of 1 1 light (compared to ) allows it n sinθ= n sin θ to be switched rapidly 1122 and carry more

nsin902 (1.0)(1.0) information. sinθ=1 = = 0.66 n1.521 o θ must be > 41o θ=1 arcsin(0.66) = 41 1

A diamond sparkles due to total Dispersion internal reflection

Diamond has a high refractive • Dispersion is the separation of light with index n = 2.42 allowing total different due to the wavelength internal reflection occurs more dependence of the index of refraction of a readily .

The diamond must be cut properly θ θ = 41o

Different colors are refracted by Wavelength dependence of n different angles in a prism

For most materials n increases with decreasing wavelength

Highest in the blue region

Lowest in the red region

6 Dispersion of light by a prism . Example A prism of crown glass refracts light normally incident on one surface. For θ = 40o find the angle ∆θ between the refracted red and violet light.

violet n1 = 1.538 red n = 1.516 θ=40o 1 n=1.00 o θ1=40 θ2

θ1 nn11sinθ = sinθ 2 ∆θ sinθ = n sinθ n1 21

o θ2red = arcsin(n1red sinθ) = arcsin(1.516sin40) = 77.0

o θ2violet = arcsin(n1violet sinθ) = arcsin(1.538sin40) = 81.3 ∆θ=4.30

The shape of the is due to parallel beam of light Rainbow reflected and refracted from raindrops at a special angle (rainbow angle of 40o -42o) The colors of the rainbow are due to dispersion of the light.

A rainbow is seen on a rainy day when the sun is to your back, low in the horizon (less than 42o above the horizon) A second rainbow is often seen with the order of colors reversed.

Dispersion of light by a rain drop

Three interfaces A) Refraction B) Reflection A) C) Refraction

Violet light is refracted more B) but gives a smaller rainbow angle

C)

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