Physics 2112Unit 25 What happens at boundaries - Reflection - Refraction - Snell’s Law - Critical Angle Polarization - Brewster’s Angle
Boundaries Recall from 2111: When wave hits a boundary where speed changes - part is transmitted - part is reflected DEMO Same with E&M: Think of window. Can see through it Can see reflection in it Speed of light is different in vacuum and glass
Speed of Light in media Relative speeds given by index of refraction, n speed of light in vacuum V n = = speed of light in media C Media n vacuum 1.0 air ~1.0 water 1.33 alcohol 1.36 glass 1.5 diamond 2.4 Recall: So can think of n as:
Reflection Measured from normal
CheckPoint 2: Changes at Boundary A ray of light passes from air into water with an angle of incidence of 30 degrees. 30o • Which of the following quantities does not change as the light enters the water? • wavelength • frequency • speed of propagation • (A) and (B) • (B) and (C)
Refraction: Snell’s Law tab=Dxab/v1 tab = tdc a D b c d
Think of it another (weird) way… This one is better Not the quickest route… Minimum Travel Time What's the fastest path to the ball knowingyou can run faster than you can swim?
Not on test…. x1 A l1 y1 Same Principle works for Light! D y2 l2 x2 B Time from Ato B: To find minimum time, differentiate twrtx1 and set = 0 How is x2 related to x1? Setting dt/dx1= 0 v=c/n
REALLY(!) weird (….but not on test) This business of “minimum travel time” is everywhere in nature! Remember from 2111? When you kick a soccer ball up at 30o, where does it land? It lands so that the integral has minimum value. “Principle of Least Action” “Lagranginan”
CheckPoint 2: Refraction A ray of light is bent as it passes from medium 1 to medium 2. • Compare the indices of refraction in the two mediums. • n1 > n2 • n1 = n2 • n1 < n2
Example 25.1: Cube of Glass 25o A beam of laser light hits a cube of glass that is 4cm on a side with a angle that is 25o to the normal. The index of refraction for glass is n= 1.5. At what angle will it leave the cube? How much is the beam shifted by the cube? ? ?
Example 25.2: Fish in the water The light from a fish is incident from below on the boundary between water and air with an incident angle of 30o. At what refracted angle does it leave the boundary? 30o • What if the incident angle had been 60o?
Phet Demo Click Here for Demo
Total Internal Reflection NOTE: n1>n2impliesq2>q1 BUT:q2 has max value = 90o! q1>qc Total Internal Reflection
Example 25.3: Diver’s Ilusion If a scuba diver looks straight up towards the surface from underwater, he see a bright circle of light. Why? What is the size of that circle?
Checkpoint 2 A light ray travels in a medium with n1 and completely reflects from the surface of a medium with n2. • The critical angle depends on: • n1only • n2only • both n1 and n2
How much is reflected? When going from n1>n2, some is reflected, some is transmitted (refracted) How much goes into each? Complex. We can do extremes.
Example 25.3: Reflection from Window If you looked straight into a window made of regular glass, you would see a reflection of the things behind you. What refraction of the intensity of the original waves would in that reflected image?
Polarization Intensity decreased in plane of incidence Unpolarized Partially polarized plane of incidence
Polarization Completely polarized when Q1 + Q2= 90o Brewster’s Angle:QB= tan-1(n2/n1) Snell’s Law:
Example 25.4: Brewster’s Angle A light beam is incident on a piece of glass (n=1.5) at the minimum angle for which to reflected beam is completely polarized. What is Qr for the portion of the beam that is refracted? QB Qr
CheckPoint4 A ray of light passes from air into water with an angle of incidence of 30 degrees. 30o • Some of the light also reflects off the surface of the water. If the incident light is initially unpolarized, the reflected light will be • Unpolarized • Somewhat horizontally polarized • Somewhat vertically polarized
CheckPoint3 A light is shining at the bottom of a swimming pool (shown in yellow in the figure). A person is standing at the edge of the pool as shown. • Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection at the water-air surface? • yes • no
Dispersion Speed of E&M wave in media decreases in media slightly with frequency dispersion n is slight frequency (wavelength) dependent
Rainbows Refraction (dispersion) Mixed (white) light Raindrops reflection Refraction (dispersion) 84o
Example 25.4: Meter Stick in Tank 45o A meter stick lies at the bottom of a rectangular water tank of height 50cm. You look into the tank at an angle of 45orelative to vertical along a line that skims the top edge of the tank. nwater= 1.33 50 cm 0 20 40 60 80 100 meter stick What is the smallest number on the meter stick that you can see?
Summary from n2 to n1