Interference in Waves SPH4U – Grade 12 Physics Unit 2

Interference in Waves

SPH4U – Grade 12 Physics

Unit 2

Tribal Challenge!

A ray of light travels from glass into water. Find the angle of refraction in water if the angle of incidence in glass is 30º.

(nwater = 1.33, and nglass

= 1.5)

3 points – first team correct

1 point – every correct answer after that

Tribal Challenge!

A ray of light travels from glass into water. Find the angle of refraction in water if the angle of incidence in glass is 30º.

(nwater = 1.33, and nglass

= 1.5)

Solution:

water

glass

water

glass

n

n

sin

sin

5.1

33.1

sin

)30sin(

water

3.34water

Therefore, the angle of refraction in water is 34.3º.

Review

When two waves cross paths and become superimposed, they interact in different ways. This interaction is called interference.

Waves that build each other up have constructive interference.

Waves that cancel each other out have destructive interference.

Review

Constructive Interference Destructive Interference

Two Point Interference Pattern

When we have two identical point sources that are side by side, in phase, and have identical frequencies, we can analyse the interference pattern that is produced to learn more about the waves.

ripple tank simulation of two point source pattern: http://www.falstad.com/ripple/

Two Point Interference Pattern

Sources

NodesAntinodes

Two Point Interference Pattern In the diagram, crests

are represented by thick lines and troughs are represented by thin lines. We get constructive interference then whenever a thick line meets thick line, or when a thin line meets a thin line. This constructive interference causes antinodes, shown by the red dots.

Thick line = crest

Thin line = trough

Two Point Interference Pattern Destructive

interference occurs whenever a thick line meets a thin line. These points form nodes, which are represented by a blue dot. The nodes and antinodes appear to ‘stand still’ which makes this a standing wave pattern.

Two Point Interference Pattern The antinodes and

nodes seem to all be located on lines. These are called antinodal lines and nodal lines, respectively. There is a central line in the pattern, the line that bisects the line segment drawn between the two sources. This is called the central antinodal line.

Central antinodal line

Two Point Interference Pattern The antinodes and

nodes seem to all be located on lines. These are called antinodal lines and nodal lines, respectively. There is a central line in the pattern, the line that bisects the line segment drawn between the two sources. This is called the central antinodal line.

Central antinodal line

Two Point Interference Pattern The number of nodal

lines increases when you do any of the following: Increase frequency of the

sources Decrease the wavelength

of the waves Increase separation

between the sources

Mathematical Analysis If we have a

two point source interference pattern like this one we can analyse it mathematically in order to determine the wavelength of the waves.

1st nodal line, n1

2nd nodal line, n1

n3

The nodal lines are measured from the central antinodal line outward.

Mathematical Analysis Let’s put a

point P1 somewhere on the first nodal line. We can measure the path length between each source and this point. These are the blue and red lines.

AP1

Mathematical Analysis The path

difference, Δs is the difference between the length of the blue and red lines. On the first nodal line, the path difference equals ½ λ.

P1

Δs = |P1S1 – P1S2| = ½ λ

This equation works for points that are on the first nodal line only

Mathematical Analysis In general, we

can find the path difference for a point on any nodal line using the equation below:

P1

Δs = |P1S1 – P1S2| = (n-½) λ

This equation works for points that are on the nth nodal line, only if the wavelengths are large enough or if the point P is not too far away from the sources.

Mathematical Analysis

If the point P1 is very far away compared to the distance between the sources, we can use this equation:

P1

λ = wavelength n = nth nodal line d = distance between S1 and S2

θn = angle between the central line and the nth nodal line

dnn

2

1sin

θn

d

Mathematical Analysis Note that due to

trigonometry, you can also find θn using basic trigonometry:

P1



θn

d

L

xnn sin

xn

L

Mathematical Analysis This of course implies the

following equation to be true:

P1



θn

d

xn

L

dn

L

xn

2

1

Example 1

Two identical point sources 5.0cm apart, operating in phase at a frequency of 8.0Hz, generate an interference pattern in a ripple tank. A certain point on the first nodal line is located 10.0cm from one source and 11.0cm from the other. What is the wavelength of the waves?

Example 1

Two identical point sources 5.0cm apart, operating in phase at a frequency of 8.0Hz, generate an interference pattern in a ripple tank. A certain point on the first nodal line is located 10.0cm from one source and 11.0cm from the other. What is the wavelength of the waves?

Young’s Double Slit Experiment

Young’s Double Slit experiment, conducted at the end of the 1700’s, is famous because it showed that light created an interference pattern that resembled the interference of water waves in a ripple tank.


Videos: Derek Owens:

http://www.youtube.com/watch?v=AMBcgVlamoU

Dr. Quantum: http://www.youtube.com/watch?v=Q1Yqg

PAtzho


The experiment showed that light coming from the two slits interfered with itself to create constructive and destructive interference.


Where we have constructive interference we get brighter bands of light, and where there is destructive interference we get bands of darkness.


People had tried to do this experiment prior to Young, but their attempts had failed because the sources they had used were too far apart, and were out of phase with each other.


Young fixed these problems by using one source, the sun, and then splitting that light using a screen to make two sources. He also made the holes for S1 and S2 very close together. This allowed an interference pattern to be visible even though the wavelength of light is very small. (about 400-800 nano meters).


The fact that light passing through the two slits acted like point sources that created circular waves, was further evidence of diffraction (bending) of light.

The experiment as a whole was strong evidence of the wave nature of light. At this point the wave theory could explain all properties of light except for propagation through a vacuum.


The experiment also provided a way to measure the wavelength of light, using the same equations we just derived for a two point source interference pattern.

In young’s experiment, a nth order dark fringe would be at a location

Ld

nxn

2

1


We can also use the following equation to calculate the wavelength of light in Young’s experiment:

Δx is the distance between adjacent dark lines L is the distance from the two sources of light to the screen d is the distance between the two sources of light λ is the wavelength of light

dL

x

Example 2

You are measuring the wavelength of light from a certain single-colour source. You direct the light through two slits with a separation of 0.15mm, and an interference pattern is created on a screen 3.0m away. You find the distance between the first and the eighth consecutive dark lines to be 8.0cm. At what wavelength is your source radiating?

Example 2

You are measuring the wavelength of light from a certain single-colour source. You direct the light through two slits with a separation of 0.15mm, and an interference pattern is created on a screen 3.0m away. You find the distance between the first and the eighth consecutive dark lines to be 8.0cm. At what wavelength is your source radiating?

Homework

Prepare for tomorrow’s lab Read Section 9.3 & 9.5

Make additional notes to supplement the lesson notes. Complete the following questions:

What is “Poisson’s Bright spot”? How did it’s discovery help to solidify the scientific view that light behaved like a wave?

Pg. 468 # 2,3 Pg. 484 # 2, 4, 5

Documents

Interference in Waves SPH4U – Grade 12 Physics Unit 2