9.3 Interference

Monochromatic light of wavelength λ is incident on a double slit. The resulting interference pattern is observed on a screen a distance p from the slits. The distance between consecutive fringes in the pattern is 21 mm when the slit separation is q.

λ and q are tripled and p is doubled. 

What is the new distance between consecutive fringes?

A transparent plastic forms a parallel-sided thin film in air. A ray X is incident on the upper-air plastic boundary at a normal incidence is shown on the diagram. 

Reflections from the top and bottom surface of the film result in three rays P, Q and R. An observer can see a whole spectrum of colours at the point PQR. 

Which path differences are correct for the minimum thickness of the plastic? 

	X - P	X - Q	P - R
A.			0
B.		0
C.	0
D.

A ray of light is incident on the boundary between two materials n₁ and n₂ where n₁ < n₂.

Which diagrams show the correct behaviour of this ray of light at the boundary?

The figure below shows a spectrometer that uses a diffraction grating to split a beam of light into its constituent wavelengths and enables the angles of the diffracted beams to be measured.

Light with a particular wavelength is passed through the diffraction grating. The angle of diffraction θ at the centre of the observed beam at Z in the image above is 45⁰ where sin(45) =  and the grating has 1000 lines per mm.

A dark fringe is observed at position W, with the central maximum at the straight-through position.

How many orders of maxima of this light are present at this wavelength?

A diffraction grating is illuminated normally with light of wavelength 5 x 10^-7m.

When a screen is 1 m from the grating, the distance between the zero and first-order maxima on the screen is 0.20 m.

You may need to use the following values in your calculation:

What is the number of lines per mm of the diffraction grating?

A Physicist carried out Young's double slit experiment using a monochromatic beam. The diagram shows the equipment set-up and the pattern produced with a ruler next to it. 

What is the wavelength of the monochromatic beam? 

The diagram below shows an arrangement used to investigate double-slit interference using microwaves.

The diagram below shows the view from above.

The microwaves from the transmitter are polarised. These waves are detected by the aerial in the microwave detector. The aerial is a vertical metal rod.

The detector is moved along the dotted line HL. As it is moved, maximum and minimum signals are detected. Maximum signals are first detected at points I and J. The next maximum signal is detected at position K.

The distances between each of the two slits, S₁ and S₂ and the microwave receiver when the aerial is in position K are S₁K = 0.1115 m and S₂K = 0.0315 m

 Which of the following reasons explains why the signal strength falls to a minimum between H and I, and between I and J?

	Reason 1	Reason 2	Reason 3
A.	Waves are out of phase	Gives rise to a path difference	Destructive interference occurs
B.	Waves are out of phase	Gives rise to a path difference	Constructive interference occurs
C.	Path difference for the two waves	Gives rise to a phase difference	Constructive interference occurs
D.	Path difference for the two waves	Gives rise to a phase difference	Destructive interference occurs

White light is passed through a double slit and an interference pattern is observed on a screen 2.0 m away. The separation between the slits is 0.5 mm. The first violet and red fringes are formed 2.0 mm and 3.0 mm respectively away from the central white fringe.

What are the wavelengths of the violet and red light?

A parallel beam of monochromatic light is directed normally at a plane of transmission grating which has N slits per meter.

The second-order diffracted beam is at an angle θ to the zero-order transmitted beam.

 

The grating is then replaced by a plane transmission grating which has 5N slits per meter.

Which one of the following statements is correct?

The diagram below shows an arrangement for a two-slit interference experiment. Coherent light of frequency f is incident on two narrow parallel slits S₁ and S₂. An interference pattern is observed on a screen a distance away. The central bright fringe is at O and the next bright fringe is at P. The speed of light is c.

The distance S₂P – S₁P is equal to

The interference of light waves is observed using a double-slit arrangement as shown below.

 

Which of the following best shows the intensity distribution of light at point O on the screen?

In an experiment, light incident on a diffraction grating has a first maximum of the second order in the same location as the first minimum of a single slit diffraction pattern. The light source and the distance from the slits to the screen are kept the same. 

What is the relationship between the slit separation d and the slit width b? 

The graph shows the intensity pattern from the interference of monochromatic light passing through N slits. 

Which row gives the correct value of N and the correct relationship between the slit separation d and the wavelength λ?

	N	Relationship
A.	6	d =
B.	6	d = 2λ
C.	4	d = 2λ
D.	4	d =

Monochromatic light of wavelength, 6λ is incident on a thin film of transparent plastic with a refractive index 1.5n. The film is surrounded by air. The intensity of the light observed reflected off the film is a minimum. What is a possible thickness of the plastic? 

Red light is incident on a diffraction grating, a double-slit and a single-slit. The patterns produced on a screen some distance away are shown below.

Which row in the table correctly identifies patterns p, q and r?

	p	q	r
A.	Diffraction Grating	Double Slit	Single Slit
B.	Double Slit	Single Slit	Diffraction Grating
C.	Single Slit	Double Slit	Diffraction Grating
D.	Diffraction Grating	Single Slit	Double Slit

Which of the following statements about thin film interference are correct?

I. A phase change occurs at a boundary between a more dense and a less dense material

II. A phase change always involves some reflection and transmission

III. The wavelength of a wave transmitted between materials of different densities stays the same

IV. Light in a thin film travels a distance of two times the thickness of the film when it enters and leaves the film at the same surface to undergo destructive interference

The graph shows the variation with diffraction angle of the intensity of light when monochromatic light is incident on a diffraction grating. 

The number of slits is reduced to less than 20. The width and the separation of the slits remain the same. 

Three possible changes to the pattern are: 

I. The intensity of the primary maxima increases 

II. The width of the primary maxima increases 

III. Secondary maxima are seen between the primary maxima 

Which of the possible changes are correct?

A beam of monochromatic light is incident normally on a double slit. The slit spacing is d. The angles between the different orders are shown on the diagram. 

What is the expression for the wavelength of light used?