Interference and Young's double slit

Monochromatic light of wavelength λ is used in a double-slit experiment. The slits are vertical and have a separation s. A narrow screen of width Y is placed a distance D from the slits.

Which gives the number of fringes observed on the screen?

Point sources of sound of the same frequency are placed at S₁ and S₂.

A sound detector is moved slowly along the line PQ. Consecutive maxima of sound intensity are detected at W and Y and consecutive minima are detected at X and Z.

What is the wavelength of the sound?

Monochromatic light is used in a Young’s double-slit interference experiment after passing through a single slit. The resulting fringe pattern is observed on a screen.

The separation of the fringes can be increased by

A double slit with a separation s is illuminated by light of wavelength λ. Fringes with spacing w are produced on a screen placed a distance D from the slits.

Which combination of slit separation and wavelength produces a fringe spacing of 1.5 w on

Light of wavelength 5.2 × 10⁻⁷ m is used in a Young’s double-slit experiment. The distance from the slits to the screen is 1.5 m. The width of ten fringes is 3.5 cm.

What is the separation of the two slits?

Figure 1 shows apparatus used to investigate the properties of microwaves. The microwaves from the transmitter T are vertically polarised and have a wavelength of about 3 cm. The microwaves are detected at the receiver by a vertical metal rod R.

Explain how the apparatus can be used to demonstrate that the waves from T are vertically polarised.

Figures 2a and 2b show T and R and two different positions of a metal plate M that reflects microwaves. M is vertical and parallel to the direct transmission from T to R.

In an experiment, T and R are about two metres apart. M is moved slowly towards X Figure 2a shows the initial position of M. Figure 2b shows M when it has been moved a few centimetres.

The arrowed lines show the path of waves that reach R directly and the path of waves that reach R by reflection from M.

Explain what happens to the signal detected by R as M is moved slowly towards X.

Figure 3 shows an arrangement used in a different experiment to try to determine the wavelength of the microwaves.

A double-slit arrangement is placed between T and R.

The initial position of R is the same distance from each slit and is 0.45 m from the midpoint of the two slits. AB is a line perpendicular to the line between T and the initial position of R. R can be moved 0.25 m towards A and 0.25 m towards B along AB.

The two slits act as two coherent sources with a separation of 0.12 m.

Suggest why Young’s double-slit equation should not be used to determine the wavelength.

The wavelength is known to be about 3 cm.

Deduce whether this practical arrangement is suitable for a determination of a value for the wavelength.

A student investigates the interference of sound waves using two loudspeakers, P and Q, connected to a signal generator (oscillator). Each loudspeaker acts as a point source of sound.

Figure 3 shows the arrangement.

Point O is the midpoint between P and Q.

Explain why the two loudspeakers are coherent sources of sound waves.

The student faces the two loudspeakers at point A. Point A is at equal distances from P and Q. He then moves to point B, at right angles to the line OA, still facing the two loudspeakers. As his head moves from A to B the amplitude of the sound wave he hears decreases and then increases. The amplitude starts to decrease again as he moves beyond B.

Explain why the variation in amplitude occurs as he moves from A to B.

The student records the following data:

separation of the two loudspeakers = 0.30 m distance OA = 2.25 m distance from A to B = 0.95 m

Show that the path difference for the sound waves from the two loudspeakers to point B is about 0.1 m.

The frequency of the sound wave is 2960 Hz.

Calculate the speed of sound from the student’s data.

The student moves his head to point C as shown in Figure 4. The emitted frequency of the sound from the loudspeakers is then gradually decreased.

Discuss the effect that this decrease in frequency has on the amplitude of the sound wave heard by the student.

In the diagram, P is the source of a wave of frequency 50 Hz

The wave travels to R by two routes, P → Q → R and P → R. The speed of the wave is

What is the path difference between the two waves at R in terms of the wavelength λ of the waves?

Light from a point source passes through a single slit and is then incident on a double-slit arrangement. An interference pattern is observed on the screen.

What will increase the fringe spacing?

One slit is then covered with opaque black paper.

What is the effect of covering one slit on the resulting interference pattern?

A microwave transmitter T and a receiver R are arranged on a line marked on the bench.

A metal sheet M is placed on the marked line perpendicular to the bench surface.

Figure 1 shows side and plan views of the arrangement. The circuit connected to T and the ammeter connected to R are only shown in the plan view.

The distance y between T and R is recorded.

T is switched on and the output from T is adjusted so a reading is produced on the ammeter as shown in Figure 2.

M is kept parallel to the marked line and moved slowly away as shown in Figure 3

The reading decreases to a minimum reading which is not zero. The perpendicular distance x between the marked line and M is recorded.

The ammeter reading depends on the superposition of waves travelling directly to R and other waves that reach R after reflection from M.

State the phase difference between the sets of waves superposing at R when the ammeter reading is a minimum. Give a suitable unit with your answer.

Explain why the minimum reading is not zero when the distance x is measured.

When M is moved further away the reading increases to a maximum then decreases to a minimum.

At the first minimum position, a student labels the minimum n = 1 and records the value of x. The next minimum position is labelled n = 2 and the new value of x is recorded. Several positions of maxima and minima are produced.

Describe a procedure that the student could use to make sure that M is parallel to the marked line before measuring each value of x. You may wish to include a sketch with your answer.

It can be shown that

The student plots the graph shown in Figure 4.

and adds error bars to the graph.

Determine

the maximum gradient G_max of a line that passes through all the error bars

the minimum gradient G_min of a line that passes through all the error bars.

Explain how the graph in Figure 4 can be used to obtain the value of y. You are not required to determine y.

Suppose that the data for n = 13 had not been plotted on Figure 4.

Add a tick () in each row of Table 1 to identify the effect, if any, on the results