A model of a lens
Classroom Activity for 14-16
What the Activity is for
Making a lens with string.
This is set up as a bench top experiment, but really it's a piece of practical mathematics. If run well, it can drive home the function of
do like me, but later, trip time, and therefore geometry in the design and explanation of lens action.
What to Prepare
- several trip time rulers (these will be different colour rulers, marked out in nanoseconds – you might choose yellow to mark out the times to cover respective distances in glass, and green to mark out those in air)
- a large piece of paper, suited to the scale of the rulers
- an optical smoke box, for demonstrating lens action
- perhaps 3 cm waves and wax lenses
What Happens During this Activity
Start out by marking out a source and a detector on the large piece of paper. Explain that the purpose of the very special optical device we are going to design is to ensure that by whatever path the light travels from source to detector, the contributions from different paths will be in step at the detector. You're likely to have to revise the idea of what it means to be in step – simple enactment like hands going up and down together can be evocative and interactive here. Link this to the instruction to do like me, but later, and draw out the importance of trip time.
Now sketch out some possible paths for the light as it passes from the source to the detector. The argument then needs to be developed as follows.
The one that takes the least time, directly from source to detector, is the one that presents most problems. Any other path will take longer, so somehow we need to increase the length of time between the source and the detector for this path. Any suggestions – can anybody think how we can make light take longer to get from the source to the detector? Draw out the idea that the trip time for each centimetre, millimetre, or metre is greater in glass than in air. So inserting extra glass in this path will increase the trip time.
Now focus on paths defined by waypoints at the top and the bottom of the paper. These will necessarily take a very long time, because there is a great distance to be covered. For these paths, therefore, you want no glass in the way and the light to be travelling through the air for the entire path.
Paths that have waypoints between the extremities and the centre will require the insertion of the lengths of glass somewhere between zero and the length inserted for the direct path, in order to compensate for the shorter distances that the light has to cover in traversing the more direct parts.
Now reinforce this hand-waving argument, by using the rulers to measure the lengths of time and make them equal. In this way it's possible to work out exactly how much glass has to be inserted. Joining up the required lengths of glass, denoted by the appropriately coloured rulers, with a smooth curve will reveal a focusing lens.
To go with this you'll want a good lens demonstration, such as that provided by a smoke box, which you can find on practicalphysics.org. You might also have access to wax lenses for 3 cm waves. These can be impressive. And emphatically make the point that the mechanism works across many different frequencies.