Chapter15 Section 1 Interference

Objectives

• Describe how light waves interfere with each other to produce bright and dark fringes.

• Identify the conditions required for interference to occur.

• Predict the location of interference fringes using the equation for double-slit interference.

What is interference

• Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium

• Interference takes place only between waves with the same wavelength. A light source that has a single wavelength is called monochromatic.

Types of wave interference

• This type of interference is sometimes called constructive interference. Constructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses. Constructive interference is observed at any location where the two interfering waves are displaced upward. But it is also observed when both interfering waves are displaced downward

Constructive interference example

In this case, a sine pulse with a maximum displacement of -1 unit (negative means a downward displacement) interferes with a sine pulse with a maximum displacement of -1 unit. These two pulses are drawn in red and blue. The resulting shape of the medium is a sine pulse with a maximum displacement

Types of Interference

• Destructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine pulse with a maximum displacement of +1 unit meets a sine pulse with a maximum displacement of -1 unit, destructive interference occurs. This is depicted in the diagram below.

Example of destructive interference

Combining Light Waves

• Waves must have a constant phase difference for interference to be observed.

• Coherence is the correlation between the phases of two or more waves.

– Sources of light for which the phase difference is constant are said to be coherent.

– Sources of light for which the phase difference is not constant are said to be incoherent.

Demonstrating Interference

• Interference can be demonstrated by passing light through two narrow parallel slits.

• If monochromatic light is used, the light from the two slits produces a series of bright and dark parallel bands, or fringes, on a viewing screen.

Conditions for interference

Demonstrating Interference

• The location of interference fringes can be predicted.

• The path difference is the difference in the distance traveled by two beams when they are scattered in the same direction from different points.

• The path difference equals dsin.

Demonstrating

Demonstrating interference

• The number assigned to interference fringes with respect to the central bright fringe is called the order number. The order number is represented by the symbol m.

• The central bright fringe at q = 0 (m = 0) is called the zeroth-order maximum, or the central maximum.

• The first maximum on either side of the central maximum (m = 1) is called the first-order maximum.

Equations

• Equation for constructive interferenced sin = ±m m = 0, 1, 2, 3, …

The path difference between two waves =

an integer multiple of the wavelength

• Equation for destructive interferenced sin = ±(m + 1/2) m = 0, 1, 2, 3, …

The path difference between two waves =

an odd number of half wavelength

Interference example

• The distance between the two slits is 0.030 mm. The second-order bright fringe (m = 2) is measured on a viewing screen at an angle of 2.15º from the central maximum. Determine the wavelength of the light.

Solution

Interference

1. Define

Given: d = 3.0 10–5 mm = 2

= 2.15º

Unknown: = ?

Diagram:

Solution

Interference

2. Plan

Choose an equation or situation: Use the equation for constructive interference.

d sin = m

Rearrange the equation to isolate the unknown:

d sinm

Solution

3. Calculate

Substitute the values into the equation and solve:

–5

–7 2

2

3.0 10 m sin2.15º

2

5.6 10 m 5.6 10 nm

5.6 10 nm

Problem

Two slits are 0.05 m apart. A laser of

wavelength 633nm is incident to the slits.

A screen is placed 2m from the slits.

a) Calculate the position of the first and second bright fringe.

b) What is the maximum number of destructive interference spots there can be on either side of the central maximum?

videos

• Let’s watch some videos

Homework

• DO problems 1-4 in your book pg. 567

Closure

• Today we learned about interference

• Next class we are going to continue with chapter 15