Cylindrical mirror, aberration and caustic curve

Class practical

The caustic curve and how the aberration can be reduced by reducing the aperture.

Apparatus and materials

For each student or group of students

Low voltage power supply for lamp

Multi-slit screen (comb)

Cylindrical concave mirror

Large sheet of white paper (A3)

Plain card

Card with slot (see technical notes)

Barriers

Health & Safety and Technical notes

Many ray boxes of traditional design become very hot after a lesson of use. Warn the class and provide heat-proof gloves or cloths if they need to handle the ray box when still hot.

1 Suitable mirrors are available from a number of suppliers e.g. Griffin Education and Technology Supplies.

2 Some manufacturers provide a five slit screen with the ray box. However, more slits than this will make the experiment more impressive. With home made slits it is important to ensure that the slits are parallel and perpendicular, or the rays produced may appear crooked.

3 The card with slot should be large enough to block out all light from the ray box, but with a central slot that will allow three rays to pass through. Less effective would be to replace the multi-slit screen with the conventional three slit screen provided with the ray box.

Procedure

a Place the lamp and multi-slit on the sheet of paper to make a wide fan of rays. Place a (concave) cylindrical mirror in this fan. The mirror must have a large aperture (at least 120°, and preferably 180°) so that it forms a caustic curve on the paper. Slide the plain card in front of the comb as an obstruction to cut off ray after ray.

b Now use the card with the wide slit in it, in front of the comb, so that a narrow fan of rays hits the mirror and forms an image. If the card is moved across the comb, the image will slide around the caustic curve.

Teaching notes

1 This is FA Meier's famous mirror and comb experiment. Students will see a caustic curve, which they will ever afterwards recognize as the curve on the tea or coffee in a cup. It's a delight; the diagrams do not do it justice.

2 The image using the multi-slit screen will show spherical aberration. Reducing the aperture with a wide slit reduces this. Using only three rays makes it appear that the aberration has been removed.

3 If you are using a shiny metal mirror it can be turned round and the convex mirror investigated.

4 Another look at the concave mirror in the smoke box would be a good idea now. See the experiment Real an virtual images in a smoke box
This experiment was safety-checked in January 2007