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CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
College Physics B - PHY2054C
Optics: Reflection & Refraction
10/20/2014
My Office Hours:Tuesday 10:00 AM - Noon
206 Keen Building
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Outline
1 Geometrical Optics
2 ReflectionImage Formation
3 RefractionSnell’s LawTotal Internal Reflection
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Introduction
The study of light is called Optics.
Light is an electromagnetic wave and its wave nature needs tobe accounted for.
Many applications depend on the ability of lenses and mirrorsto focus light.
• Study of optics dates back to at least third century BC.
• Eyeglasses were invented around 1300.
• Microscopes and telescopes were invented around 1600.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Geometrical Optics
Geometrical optics applies to the regime where light travels instraight-line paths:
• Describes cases in which the wavelength of the light ismuch smaller than the size of objects in the light’s path.(Wavelength of visible light is less than 1 µm.)
• Effects involving wave interference are not important.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Geometrical Optics
Rays indicate the path and directionof propagation of the light wave:
A The waves pass through alarge opening and, to a verygood approximation, followstraight lines that pass throughthe opening.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Geometrical Optics
Rays indicate the path and directionof propagation of the light wave:
A The waves pass through alarge opening and, to a verygood approximation, followstraight lines that pass throughthe opening.
B The opening is about thesame size or smaller than thewavelength of the light andneeds wave optics to explain.
➜ Interference effects
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Ray Tracing
Light from an object is used by youreye to form an image of the object:
• The light waves associated withall the rays contribute to theimage formed by your eye.
• In most ray diagrams, we drawjust a few rays from the top andbottom of the image.
The motion of light along a light ray isreversible.
• If light can travel in one directionalong a ray that connects pointA to point B, then light can alsopropagate in reverse direction,from B to A.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Image Formation
Two problems must be considered to understand how imagesare formed:
1 What happens to light rays when they reflect from asurface such as a mirror or a piece of glass?
2 What happens to light rays when they pass across asurface from one material to another such as when theypass from air into a piece of glass?
➜ We must also distinguish between a flat surface and acurved surface.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Outline
1 Geometrical Optics
2 ReflectionImage Formation
3 RefractionSnell’s LawTotal Internal Reflection
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 1
A ray of light is incident on a plane mirror and the angle ofreflection is 50◦. What is the angle between the incident rayand the reflected ray?
A 50◦
B 25◦
C 90◦
D 100◦
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 1
A ray of light is incident on a plane mirror and the angle ofreflection is 50◦. What is the angle between the incident rayand the reflected ray?
A 50◦
B 25◦
C 90◦
D 100◦
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Reflection from a Plane Mirror
Light rays travel in straight lines until they strike something. Ifthe light is a plane wave, all the rays are parallel and strike asurface at many different points.
• Reflection can be characterized by a single ray.
• Normal (vertical dashed line) is perpendicular to mirror.
• The direction of the incoming and outgoing rays aremeasured relative to the normal.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Reflection from a Plane Mirror
The incoming ray is called the incident ray. The outgoing rayis called the reflected ray.
• The Law of Reflection says:
θi = θr
• Reflection from a perfectly flat mirror is called specularreflection.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Diffuse Reflection
If the reflecting surface isrough, the reflections fromeach individual piece of thesurface must be analyzed.
An incident plane wave willgive rise to many reflectedrays propagating outward inmany different directions.
➜ Diffuse reflection.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Example
Reflection from two mirrors thatform a right angle.
Law of Reflection:
θ i 2= 90◦
− θ r = 90◦− θ i
θ r 2 = θ i 2= 90◦
− θ i
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Example
Reflection from two mirrors thatform a right angle.
Law of Reflection:
θ i 2= 90◦
− θ r = 90◦− θ i (1)
θ r 2 = θ i 2= 90◦
− θ i (2)
Solve:
θ out = 90◦− θ r 2
= 90◦− (90◦
− θ i)
θ out = θ i
The outgoing ray is parallel tothe incident ray.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Image Formation
The rays that reflect from themirror and reach your eyesform the image.
There is an infinite numberof rays emanating from eachpoint on the object:
• Two representative raysare shown coming fromthe object.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Image Formation
Characteristics of the image:
• Distance from the objectto the mirror is the sameas distance from imageto the mirror.
• The size (height) of theimage, hi , is the sameas the size (height) ofthe object, ho.
• The image is virtual:• The image point is
located behind themirror.
• The light does notactually pass throughthe image.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 2
An object placed 2 m from a plane mirror is shifted by 0.5 maway from the mirror. What is the distance between the objectand its image?
A 2.0 m
B 1.5 m
C 5.0 m
D 3.0 m
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 2
An object placed 2 m from a plane mirror is shifted by 0.5 maway from the mirror. What is the distance between the objectand its image?
A 2.0 m
B 1.5 m
C 5.0 m
D 3.0 m
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 3
A plane mirror forms an image that is
A real and upright.
B virtual and upright.
C real and upside down.
D virtual and upside down.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 3
A plane mirror forms an image that is
A real and upright.
B virtual and upright.
C real and upside down.
D virtual and upside down.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Outline
1 Geometrical Optics
2 ReflectionImage Formation
3 RefractionSnell’s LawTotal Internal Reflection
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Refraction
When a light ray strikes a transparent material, some of thelight is reflected and some is refracted.
➜ The reflected ray obeys the Law of reflection.
The refracted ray passes into the material.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Refraction
When a light ray strikes a transparent material, some of thelight is reflected and some is refracted.
➜ The reflected ray obeys the Law of reflection.
The refracted ray passes into the material.
• The incident angle isnow denoted as θ1.
• The direction of therefracted ray ismeasured by using θ2.
Value of this angle dependson the incident angle and thespeed of light in the material.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 4
When a light wave enters into a medium of different opticaldensity,
A its speed and frequency change.
B its speed and wavelength change.
C its frequency and wavelength change.
D its speed, frequency, and wavelength change.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Question 4
When a light wave enters into a medium of different opticaldensity,
A its speed and frequency change.
B its speed and wavelength change.
C its frequency and wavelength change.
D its speed, frequency, and wavelength change.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Snell’s Law
The change in the speed of light from the vacuum to the materialchanges the direction of the wave:
sin θ 1 =ctL
and sin θ 2 =vtL
→
ctsin θ 1
=vt
sin θ 2
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Snell’s Law
The change in the speed of light from the vacuum to the materialchanges the direction of the wave:
sin θ 1 =cv
sin θ 2
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Snell’s Law
The ratio c/v is called index of refraction and is denoted by n:
• n = c/v ➜ sin θ 1 = n sin θ 2
A more general statement can be applied to any two materialswith indices of refraction n1 and n2:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Index of Refraction
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Snell’s Law
Snell’s Law applies whether light begins in the material with thelarger or smaller index of refraction. Refraction is reversible:
• Possible angles of refraction are between 0◦ and 90◦.
• Side with larger index of refraction has smaller angle.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Snell’s Law
Snell’s Law applies whether light begins in the material with thelarger or smaller index of refraction. Refraction is reversible:
• Light is refracted toward the normal when moving into thesubstance with the larger index of refraction.
• Light is refracted away from the normal when moving intothe substance with the smaller index of refraction.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Snell’s Law
Snell’s Law applies whether light begins in the material with thelarger or smaller index of refraction. Refraction is reversible:
• Light is refracted toward the normal when moving into thesubstance with the larger index of refraction.
• Light is refracted away from the normal when moving intothe substance with the smaller index of refraction.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Total Internal Reflection
When light is incident from the side with a higher index of re-fraction, it is bent away from the normal according to:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
What happens at θ 2 = 90◦ ?
θ 2 > θ 2
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Total Internal Reflection
When light is incident from the side with a higher index of re-fraction, it is bent away from the normal according to:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
θ 2 = 90◦ ➜ θ 1 = θ crit : θ crit = sin−1 n 2n 1
θ 2 > θ 2
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Total Internal Reflection
When light is incident from the side with a higher index of re-fraction, it is bent away from the normal according to:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
θ 2 = 90◦ ➜ θ 1 = θ crit : θ crit = sin−1 n 2n 1
The angle of incidence for which the angle of refraction is 90◦
is called the critical angle:
• If the angle of incidence is increased beyond the criticalangle, Snell’s Law has no solution for θ 2.
• This behavior is called total internal reflection.
➜ Physically, there is no refracted ray.
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Total Internal Reflection
When light is incident from the side with a higher index of re-fraction, it is bent away from the normal according to:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
θ 2 = 90◦ ➜ θ 1 = θ crit : θ crit = sin−1 n 2n 1
CollegePhysics B
GeometricalOptics
ReflectionImage Formation
RefractionSnell’s Law
Total InternalReflection
Total Internal Reflection
When light is incident from the side with a higher index of re-fraction, it is bent away from the normal according to:
n 1 sin θ 1 = n 2 sin θ 2 Snell′s Law
θ 2 = 90◦ ➜ θ 1 = θ crit : θ crit = sin−1 n 2n 1
The optical fibers arecomposed of speciallymade glass:
• These signals aresent as light waves.
• They are directedalong fiber usinginternal reflection.
