# Lloyd's mirror

This is another method for finding the wavelength of light by the division of wavefront.

Light from a slit So falls on a silvered surface at a very small grazing angle of incidence as shown in the diagram (Figure 1). A virtual image of So is formed at S1.

Interference occurs between the direct beam from So to the observer (0) and the reflected beam The zeroth fringe will be black because of the phase change due to reflection at the surface.

An interesting application of this effect may be observed when a helicopter flies above the sea near a radio transmitter.
The helicopter will receive two signals:
(a) one signal directly from the transmitter and
(b) a second signal after reflection from the sea
As the helicopter rises the phase difference between the two signals will alter and the helicopter will pass through regions of maxima and minima.

Problems
1. Would you expect to observe beats between the light from:
(a) two small monochromatic torch bulbs, (b) between two lasers?
When a converging lens is placed between a bi-prism and the eyepiece two positions can be found which give two clear images of the slit. The distance between these images is 3.73 mm and 1.24 mm respectively

2. In a Lloyd's mirror experiment the source slit So and its virtual image S1 lie in a plane 0.20 m behind the left edge of the mirror. The mirror is 0.3 m long and a screen is placed at the right edge. Calculate the distance from this edge to the first maximum if the perpendicular distance from So to the mirror is 2 mm and the light used has a wavelength of 600 nm. Calculate the wavelength of the light used in the experiment.

3. In an experiment with Fresnel's bi-prism the fringe width as measured with a micrometer eyepiece is 0.02 cm and the distance between the source slit and the cross-wires of the eyepiece is 75 cm. Calculate the wavelength off the light used.

4. Find the value of m for which the (m + 1)th blue fringe coincides with the m th red fringe in a Young's slits experiment if the separation of the slits is 0.5 mm and they are 1.2 m from the screen. Take the wavelength of red light as 780 nm and that of blue light as 520 nm.

5. Calculate the slit separation needed to produce fringes of width 0.2 mm at a distance of 0.35 m from the slits using light of wavelength 580 nm.

Student investigation
Set up the apparatus as shown below and measure the wavelength of the laser light. You should be able to see the single slit diffraction pattern crossing the cos2 fringes produced by interference. The Young's double slit experiment is much easier to perform if a laser is used as the source. The brightness of the beam makes the interference pattern visible some metres from the double slit and therefore the width of a number of the fringes is easily measurable with a ruler. Consult your teacher before proceeding
Warning laser light can be dangerous.

Student investigation
The following investigations demonstrate the principle of the stellar interferometer - a device for measuring the diameter of stars or the separation of double stars.
(a) Look at a distant light bulb first through a card with a pinhole in it and then through one with two the two cases. Compare the definition of the image seen in the two cases.
(b) Set up the microwaves arrangement shown in the following diagram. The apparatus on the left should be capable of rotating about a vertical axis through the receiver.

Adjust the angle of the plates for maximum signal. Compare the sharpness of the fringe pattern recorded as the instruments on the left are rotated slightly first with only one plate A and then with both plates A and B.

Find out how a real stellar interferometer works, at both optical and radio wavelengths.

Student investigation
It has been suggested that a way to reduce the noise in a room would be to record the sound in it and then to replay it, delaying it by half a wave.
Investigate this theory using a signal generator emitting a pure tone through one speaker and a circuit for delaying the note emitted by the other speaker.
Consider the problems due to reflections at the walls of the room.