Interference

What is superposition?

#When two or more waves arrive at the same point and overlap, their amplitudes combine  

What does the principle of superposition state?

#When two or more waves overlap at a point, the displacement at that point is equal to the sum of the displacements of the individual waves

What is constructive interference?

'#When two waves are in phase, their combined effect makes the resultant wave amplitude larger

What is destructive interference?

#When two waves are in antiphase, their combined effect means they cancel each other out

What is a requirement for interference?

#Waves must be coherent

When does coherence occur?

#Coherence occurs when waves have:

• The same frequency

• A constant phase difference

What are examples of coherent light sources?

#- Monochromatic laser light 

-Sound waves from two nearby speakers emitting sound of the same frequency

What is path difference?

#The difference in distance travelled by the two waves from their sources to the point where they meet

What is the difference between path and phase difference/

• #

• Path difference compares the amount of progress made by waves along a path 

• Phase difference compares the distance between the phases (peaks and troughs) of coherent waves that are normally travelling parallel to each other at a point 

What does the path difference between two coherent waves determine?

#The path difference between two coherent waves determines whether there is constructive or destructive interference where they meet

What kind of interference occurs when there is a path difference of a whole number of wavelengths?

#Constructive interference

What kind of interference occurs when there is a path difference of a whole and a half number of wavelengths?

#Destructive interference

What are the conditions for constructive interference?

#path difference = n x lambda

What are the conditions for destructive interference?

#Path difference = (n+1/2)lambda

Why are lasers used in interference experiments?

#They form light that is:

• Coherent (have a constant phase difference and frequency)

• Monochromatic (have the same wavelength)

What does a laser produce?

-A beam of coherent monochromatic light

What are the parts of diffraction pattern produced by a laser on a screen?

• #

• Areas of constructive interference - the bright strips or fringes

• Areas of destructive interference - the dark fringes

What are examples of non-coherent light sources?

#Other sources of light, such as a filament bulb or a sodium lamp, are non-coherent, so they produce white light

What are the dangers of lasers?

#Lasers produce a very high-energy beam of light

• This intense beam can cause permanent eye damage or even blindness

What are safety precautions of lasers?

#Never look directly at a laser or its reflection

• Don’t shine the laser towards a person

• Don't allow a laser beam to reflect from shiny surfaces into someone else's eyes

• Wear laser safety goggles

• Place a ‘laser on’ warning light outside the room

• Stand behind the laser

Where does constructive interference occur in sound wave?

#Constructive interference occurs when the compressions and rarefactions from each wave line up and the sound appears louder

Where does destructive interference occur in sound wave?

#Destructive interference occurs when a compression from one wave lines up with a rarefaction from the other and vice versa. The two waves cancel each other out, so zero sound is heard. 

How can two -source interference for microwaves be detected?

#Two-source interference for microwaves (and other electromagnetic waves) can be detected with a moveable microwave detector

How can two source interference of microwave be detected?

#-The detector picks up a maximum amplitude or intensity in regions of constructive interference 

• The detector picks up a minimum or zero amplitude, so no signal in regions of destructive interference 

What is the intensity of a wave proportional to?

#The intensity of a wave (its power per unit area) is proportional to the energy transferred by the wave

• The energy transferred by a wave is proportional to the square of the amplitude

• Therefore, the intensity of a wave is proportional to the square of the amplitude 

I = kA²

• Where:

  • I = intensity of the wave in W m^–2

  • A = amplitude of the wave in metres (m)

What is energy transferred proportional to?

#The energy transferred by a wave is proportional to the square of the amplitude

What happens in Young’s double slit experiment?

#The laser light source is placed behind the single slit

• So the light is diffracted, producing two light sources at slits A and B

• The light from the double slits is then diffracted, producing a diffraction pattern made up of bright and dark fringes on a screen

What can be seen on the diffraction pattern of double slit?

• Constructive interference between light rays forms bright strips, also called fringes, interference fringes or maxima, on the screen

• Destructive interference forms dark strips, also called dark fringes or minima, on the screen

Difference in Wavelengths of fringes in Double slit experiment?

• #

• For constructive interference (or maxima), the difference in wavelengths will be an integer number of whole wavelengths

• For destructive interference (or minima), it will be an integer number of whole wavelengths plus a half wavelength

What does n represent?

#N is the order of the maxima or minima; which represents the position of the maxima away from the central maximum

What does it mean when n is equal to 0?

#n = 0 is the central maximum

What does it mean when n is equal to 1?

#n = 1 represents the first maximum on either side of the central,

What is the equation for fringe spacing?

#W = (lambda xD/s

• D is much bigger than any other dimension, normally several metres long

• s is the separation between the two slits and is often the smallest dimension, normally in mm

• w is the distance between the fringes on the screen, often in cm. This can be obtained by measuring the distance between the centre of each consecutive bright spot.

What are the features of interference pattern produced when white light is diffracted through a double slit?

#Each maximum is of roughly equal width

• The central maximum is white because each wavelength interferes here constructively 

  • There are two dark narrow destructive interference fringes on either side

Maximas of White light(Double slit experiment)

• #

• All other maxima are composed of a spectrum

• Separate diffraction patterns can be observed for each wavelength of light

  • The shortest wavelength (violet / blue) would appear nearest to the central maximum because it is diffracted the least

  • The longest wavelength (red) would appear furthest from the central maximum because it is diffracted the most

Colours of white light in double slit experiment

#The colours look blurry and further away from the central maximum, the fringe spacing gets so small that the spectra eventually merge without any space between them

What happens when maxima moves further away from the central maximum?

#the wavelengths of blue observed decrease and the wavelengths of red observed increase

Developing Theories of EM radiation

#test

What is the resolution of the equipment used in Required Practical: Young's Slit Experiment & Diffraction Gratings?

#

• Resolution of measuring equipment:

  • Metre ruler = ±1 mm

  • Vernier Callipers = ±0.01 mm

What is the independent variable of Young Double slit experiment?

#Independent variable = Distance between the slits and the screen, D

What is the dependent variable of Young Double slit experiment?

#Fringe width, w

What are the control variables of Young Double slit experiment?

• #Wavelength of laser light, λ

• Slit separation, s

What is the method of Young Double slit experiment?

1. Set up the apparatus by fixing the laser and the slits to a retort stand and place the screen so that D is 0.5 m, measured using the metre ruler

2. Darken the room and turn on the laser

3. Measure from the central fringe across many fringes using the vernier callipers and divide by the number of fringe widths to find the fringe width, w

4. Increase the distance D by 0.1 m and repeat the procedure, increasing it by 0.1 m each time up to around 1.5 m

5. Repeat the experiment twice more and calculate and record the mean fringe width w for each distance D

How can results of Young Double slit experiment be shown?

• #

• Comparing this to the equation of a straight line: y = mx

  • y = w (m)

  • x = D (m)

  • Gradient = λ/s (unitless)

 

• Plot a graph of w against D and draw a line of best fit

• The wavelength of the laser light is equal to the gradient multiplied by the slit separation, because: Gradient = wavelength / slit separation, wavelength = slit spacing x gradient

What is the aim of the young double slit experiment?

#The overall aim of this experiment is to investigate the relationship between the slit-screen distance, D, and the fringe width, w

What is the aim of the Interference by a diffraction grate practical?

The overall aim of this experiment is to calculate the wavelength of the laser light using a diffraction grating

What is the method for finding out Interference by a diffraction grate practical?

1. Place the laser on a retort stand and the diffraction grating in front of it

2. Use a set square to ensure the beam passes through the grating at normal incidence and meets the screen perpendicularly

3. Set the distance D between the grating and the screen to be 1.0 m using a metre ruler

4. Darken the room and turn on the laser

5. Identify the zero-order maximum (the central beam)

6. Measure the distance h to the two nearest first-order maxima (i.e. n = 1, n = 2) using a vernier calliper

7. Calculate the mean of these two values

8. Measure distance h for increasing orders

9. Repeat with a diffraction grating that has a different number of slits per mm

What is the equation for the diffraction grating?

#

nλ = d sin θ

here:

• n = the order of the diffraction pattern

• λ = the wavelength of the laser light (m)

• d = the distance between the slits (m)

• θ = the angle between the normal and the maxima

What is the distance between the slits in a diffraction grating equal to?

#d = 1/N

• Where

  • N = the number of slits per metre (m^–1)

What must be done to calculate the angle with the distance between maxima(h) and the distance between the slits and the Screen(D) in diffraction grating?

#tan0 = h/D —> tan^-1(h/d)

• Since the angle is not small, it must be calculated using trigonometry with the measurements for the distance between maxima, h, and the distance between the slits and the screen, D

How do we reduce systematic errors in Diffraction grating experiment?

#

• Ensure the use of the set square to avoid parallax error in the measurement of the fringe width

• Using a grating with more lines per mm will result in greater values of h. This lowers its percentage uncertainty

• Measure the distance between each bright fringe from the centre of each bright spot

How do we reduce random errors in Diffraction grating experiment?

#

• The fringe spacing can be subjective depending on its intensity on the screen, therefore, take multiple measurements of w and h (between 3-8) and find the average

• Use a Vernier scale to record distances w and h to reduce percentage uncertainty

• Reduce the uncertainty in w and h by measuring across all visible fringes and dividing by the number of fringes

• Increase the grating to screen distance D to increase the fringe separation (although this may decrease the intensity of light reaching the screen)

• Conduct the experiment in a darkened room, so the fringes are clear

What are safety considerations of diffraction grating practical?

#Lasers should be Class 2 and have a maximum output of no more than 1 mW

• Do not allow laser beams to shine into anyone’s eyes

• Remove reflective surfaces from the room to ensure no laser light is reflected into anyone’s eyes