Snell’s Law

Amount of refraction (ie. angle change) depends on:

1. the index of refraction of the two media2. the angle of incidence

This relationship is known as Snell’s Law:

n1sinθ1=n2sinθ2

n1sinθ1=n2sinθ2

where θ1 = the angle of incidence

θ2 = the angle of refraction

n1 = index of refraction for incident medium

n2 = index of refraction for refracting medium

i

r

ni

nr

Example 1: A ray of light passes from air ( n=1.00) to

water (n =1.33), with an angle of incidence of 30°.What is the angle of refraction?

na x sin 300 = nw x sin Ɵw

1.00 x ( 0.5) = 1.33 x sin Ɵw

0.5 = sin Ɵw

1.33sin Ɵw = 0.3759Ɵw = sin -1 ( 0.3759)Ɵw = 220

Example 2: Calculate the index of refraction for an

incident substance where the angle of incidence is 30°, the angle of refraction is 50.0°, and the index of refraction of the second substance is 1.50.

( n1 = 2.3 )

Review – don’t write out. Lets do together.

1. When light passes from a more optically dense medium into a less optically dense medium, it will bend _______ (towards, away from) the normal.

2. When light passes from a medium with a high index of refraction value into a medium with a low index of refraction value, it will bend _______ (towards, away from) the normal.

** The higher the value of n the more optically dense the medium is, therefore the slower the light moves.....causing the light ray to move towards the normal when going from a high n value to a low one and away from the normal when going from a low n value to a higher one.

3. In each diagram, draw the "missing" ray (either incident or refracted) in order to appropriately show that the direction of bending is towards or away from the normal.

4. Arthur’s method of fishing involves spearing the fish while standing on the shore. The actual location of the fish is shown in the diagram below. Because of the refraction of light, the observed location of the fish is different than its actual location. Where does the fish appear to be? Must Arthur aim above or below where the fish appears to be in order to strike the fish?

5. A ray of light in air is approaching the boundary with a layer of crown glass at an angle of 42.0 degrees. Determine the angle of refraction of the light ray upon entering the crown glass and upon leaving the crown glass.

1 sin 42 = n2 sin Θ2 = 1 sin Θ3

Θ3 = 42

Practice: P.438 #’s 64, 66, 69, 60

a) Θ1 = 45o

b) Θ1 = 48o

c) Θ1 = 49o

Comment on what is happening to the refracted light ray.

Calculate the angle of refraction in air when light leaves water (n=1.33) at the following angles of incidence:

Total Internal Reflection:When light goes into a less dense medium it speeds up and thus bends away from the normal.Greater than a “critical angle”, the light will not exit the medium and it will “reflect” back into medium 1.

The critical angle for a particular material is the angle of incidence for which the angle of refraction is 90o.

The symbol for critical angle is Θc.

In order for a critical angle to exist a materialmust always be optically denser than the 2nd material. ie. n1 > n2

ni

nr

c

Critical Angle

From Snell, n1 sinc = n2 sin 90

Since sin 90 = 1, we haven1 sinc = n2

and the critical angle is c = sin-1

ni

n2

Example: What is the critical angle of a block of crystal

glass (n = 1.54) sitting in air (n = 1). Don't forget, material 1 is the glass.

Answer: 40.5o

Fibre Optics

Mirage Pictures

What is the point of knowing this?..........

Some very useful inventions have resulted by taking advantage of total internal reflection....

1. Periscope (tanks, submarines,...)

2. Binoculars ◦ uses a class prism to reflect light to prevent loss of

light (pg.417)

3. Endoscopes (medical camera)◦ allows doctor to explore a patient internally without

unnecessary surgery. (pg. 417)

4. Bike reflectors (pg.417)

Assign: P.439 # 79, 80.

Diffraction (10.13)If you were to shine a laser (light of one color) at a barrier with a tiny slit (opening), what would you see on the screen?

A) a single line of lightB) a central light that gradually gets dimmer as you move outC) an alternating series of bright and dark lines that gradually gets dimmer as you move out

Answer: C)

What happens between the slit and the screen is a true mystery but we see a “diffraction pattern” on the screen, a series of bright and dark spots.

The pattern’s size and location varies with the width of the slit.

Diffraction – the bending of waves (light ) around objects or through openings.

When light passes through a single opening that is close in size to it’s wavelength, the light waves interact forming a diffraction pattern.

Diffraction – finds minima (dark spots)

Light passes through a single opening of width w.

A central bright spot is created, at center.

An alternating dark then bright pattern develops on both sides.

We use a formula to locate dark spots

n=1, 2, 3, 4, 5 ... We could locate

bright spots at n=1.5, 2.5, 3.5...

sinwn Formula for minima, ie. dark spots

Single slit - diffraction formula

n=nodal line # (minima/darkspot: n=1,2,3...)

λ = wavelength of light (m)w= width of slit (m)θ = angle away from center line (degrees)

ExampleA 20.0 µm slit is illuminated by a red light (620 nm). At what

angle is the third order minimum located ?

w = 20.0 x 10 -6 m λ = 620 x 10 -9 m n = 3 nλ=wsinθ

θ = Sin -1 (nλ/w)θ = Sin -1 (3 x 620 x 10 -9/ 20.0 x 10 -6 )θ = 5.30o

Assign p. 441 # 100 & 101.

sinwn

P.441 #s 100 and 101.

The water waves below diffract a little different than light.

Light’s Diffraction Pattern:Wave, particle orsomething else ?

https://www.youtube.com/watch?v=Iuv6hY6zsd0#t=403

Veritasium- The original double slit experiment.

Watch

Young’s Double Slit ExperimentWhen light passes through 2 small slits with a small separation (d)

between slits they may create an interference pattern. For light, crests and troughs produce bright and dark spots on a screen.

Note: 2 Formulae for Double Slit find maxima (bright spots)

n= order number (bright spot from center line)λ = wavelength of lightd= slit separation (distance between 2 slits)θn = angle from center to nth maxima

n= order number

λ = wavelength of lightd= slit separation (distance between 2

slits)xn =distance from center to nth maxima

L = distance from centre of slits to maxima

nλ = dsinθn

L

dxn n

Ex. 1:A 450 nm light passes through two slits with separation of 3.00

µm. a) Find the angle at which the second order maximum is located

on a screen 1.00 m from the slits.n = 2 λ = 450 nm = 450 x 10 -9 md = 3.00 x 10 -6 m θ2 = ?

nλ = dsinθn θ2 = sin-1 (n λ/d) = 17.5o

b) How far from the centre line is this second maximum located?

X = 0.300 m or 30.0 cm

** How would you find Minima (dark spots)? n = 0.5, 1.5, 2.5 ...Practice p. 440 #92-94.

Speed – depends on medium. Sound in Air – temperature, pressure, etc. Speed of Sound in Air vsound = 332m/s + 0.6 T

Note: T is temperature in oC Waves in string – tension, string diameter/mass

Frequency – depends on source Wave’s Frequency = Frequency of vibrating source

Wavelength (λ) – depends on Eq’n: λ = v/f

Waves:

https://www.youtube.com/watch?v=imoxDcn2Sgo

What is happening ?

The frequency of a wave does not change once created. However, if the source and observer are moving relative to each other there is an apparent change in frequency, a Doppler shift.

Doppler Effect for Sound

http://www.absorblearning.com/advancedphysics/demo/units/040103.html#Introduction

Interactive website:

Note: Doppler effect involves apparent change in

frequency observed due to relative velocity and not the change in loudness due to distance.

Doppler effect for sound:

f2 =f1vs

vs ±

vo

Where: f2 = apparent frequency (Hz) f1 = original frequency of source (Hz)vs = speed of sound (m/s)vo = relative speed of observer (m/s)+ when source/observer move apart- when source/observer move towards each other

Ex.It is 10.0 oC and you are moving toward a stationary alarm which has a frequency of 925 Hz. What is the apparent frequency you hear if you are traveling at 101 km/h ?

Answer ( 1010Hz )

Assign P. 480 # 64-66.

What is happening ?

Water vapourcondensed dueto Sonic Boom.

If the source travels faster than the wave it will pass it’s own wave causing new waves to overlap the previous ones. This gives constructive interference at a V shape behind the object.

Sonic Boom

Shock wave behind boat moving > speed of water wave

The Doppler Effect for Light

Main Applications: Radar guns Astronomy Weather Radar

An apparent shift in frequency can also occur with light waves. The difference in these frequencies tells us the speed of the object.

Formula for Radar GunsUse the following for radar guns:

Wheref2 is the measured frequency,

f1 is the emitted frequency

vr = relative velocity of object

c = speed of light

Ex. A stationary police officer uses a radar gun emitting EM waves at 9.00 x 10 9 Hz. The detected waves differ by 2000 Hz. What is the speed of the approaching car?

cf

fvr

12

12 fff

cf

fvr

128

91000.3

1000.92

2000x

xxvr

= 33 m/s

Formula for AstronomyIn astronomy the difference in colors (λ or f) is compared

when a star or galaxy is moving. The change or shift in color tells us how fast it’s traveling.

Where:f2 is the observed frequency (Hz)

f1 is the source frequency (Hz)

v = relative velocity of objectc = speed of light (3.00x108m/s)

Ex. Star ‘Swerc’ normally emits a frequency of 5.77x1014 Hz. On Earth we observe 5.76x1014 Hz. What is the speed of the star and is it moving toward or away from us?

Lower f = moving away (use – sign) Answer: (520km/s)

c

vff 112

Red shifts and Blue shiftsIn Example 1 the star is going away from the source.This is called a red shiftbecause the wavelength has shifted

toward the red end of spectrum.

The opposite would be a blue shift.

Practice P. 440 # 83,84,87