Reflection and Refraction

Reflection When a wave reaches a boundary it is: Partially reflected (bounces off surface) Partially transmitted through surface.

Law of Reflection Angle of incidence = Angle of reflection

Note The angle of incidence is formed between the incident ray and the normal. The angle of reflection is formed between the reflected ray and the normal.

Reflection Regular reflection – occurs when parallel light waves strike a surface and reflect in the same parallel directions “Smooth” surfaces Diffuse Reflection – occurs when parallel light waves strike a rough uneven surface and reflect in many different directions.

Regular Reflection A reflection produced by a smooth surface.

Diffuse Reflection Reflection from a rough surface.

Diffuse Reflection When the surface is rough, images are not formed, but the light still reflects

Regular Regular http://micro.magnet.fsu.edu/primer/java/reflection/specular/specularjavafigure1.jpg

Diffuse Reflection Bumps on the surface must be less than about 1/8 the wavelength of light in order to have a smooth surface Big satellite dishes are made of wire mesh and appear smooth to the longer wavelength microwave signals

Satellite Dish

Satellite Dish

di=do hi=ho

Type of Image Real or Virtual Enlarged or Reduced Erect or Inverted

What is the minimum mirror height required for a person to see their full self in the mirror?

Hint: Compare AB to CD C A B D

Creating Images

Plane Mirrors We trace rays from the object A plane mirror always produces a virtual image Virtual image – copy of an object formed at location from which the light rays appear to come The image is the same distance behind the mirror as the object is in front of it The object and the image are the same size

Refraction When a wave crosses a boundary between Medium 1 and Medium 2, the wave changes direction because it changes velocity. Frequency remains constant. Velocity changes as a result of wavelength change. Simulations Refraction Phet Refraction

Refraction

Refraction

Example Incident Ray Less Dense Medium More Dense Refracted Ray

Index of Refraction

Index of Refraction

Refraction When light slows down at a boundary, it bends toward the normal (less dense to more dense) When light speeds up at a boundary, it bends away from the normal (more dense to less dense)

Index of Refraction, n n>1 (Why?) n = c / v c : the speed of light in a vacuum, 3 x 108  m/sec v : speed of light in the medium. n : medium's index of refraction n>1 (Why?)

Indices of Refraction Vacuum 1.00 Air 1.0003 Water 1.33 Ethanol 1.36 Crown glass 1.52 Quartz 1.52 Diamond 2.42

Problem What is the speed of light in quartz? n = 1.54 Answer: 1.97 x 10 8 m/s

Snell’s Law n1 sin q1 = n2 sin q2

Problem What is the angle of refraction when a ray from air with an angle of incidence of 25 o is incident to water? Draw the ray diagram. Answer: 18.5 o

Total Internal Reflection Can occur when ray goes from higher n to lower n. Above a Critical angle (of incidence) the ray is reflected, not refracted http://www.walter-fendt.de/ph14e/refraction.htm For problems, set the angle of refraction to 90, and solve for critical angle

Total Internal Reflection This is used in fiber-optic cables to transmit data signals. The light inside the cable cannot escape so no energy (signal) is lost as it travels.

Why We Love Diamonds?

Total Internal Reflection in a Diamond

Problem Find the critical angle for a light ray that is incident from water to air. Answer: 48.8 o

Dispersion The index of refraction of glass is different for the colors that make up white light because the speed of light is slightly different in glass for each frequency of light. (In vacuum all colors have speed c=3x108m/s.)

As white light passes through a prism, shorter wavelengths refract more than longer wavelengths, and the colors separate Longer wavelength move faster as it enter the prism (red light) so it bends the least Violet is bent the most

Rainbows

Problem The index of refraction for crown glass for red light is 1.514. What is the speed of red light in crown glass? Answer: 1.98 x 10 8 m/s

Refraction This bending of light can play tricks on our minds

Mirages – false or distorted image

Mirage http://www.warren-wilson.edu/~physics/PhysPhotOfWeek/2007PPOW/20070921RoadMirage/IMG_1444MirageCrop500.jpg

Occurs because hot air has a lower n, than cold air.

Another Trick Light travels faster at higher altitudes because the air is less dense.