## Reflection and trip time

Classroom Activity for 14-16

What the Activity is for

In this activity, students get to explore why a reflected beam follows the path that it does. They use a physical model to carry out a mathematical experiment.

What to Prepare

- specialised cardboard rulers, measuring in nanoseconds
- outlines of reflecting objects
- a sharpened pencil

What Happens During this Activity

Start the activity by performing an impressive demonstration of reflection. It might also be a good idea to remind the students how beams reflect, by using mirrors and beams of light.

In this context, the point of these activities is to create something to be explained. Discuss the outcomes of these experiments with students so that they recognise there is something that needs a good explanatory story. You'll need to build up their expectations so that they are not happy with a simple statement of the rules. Something about the angle of reflection being equal to the angle of incidence should be the starting point and not the endpoint.

Teacher: Here's a puzzle – why does the beam follow the path that it does, as it reflects?

Perhaps there is something rather special about the path that it does follow. You might suggest that the light follows the shortest path – that is, the path with the shortest distance. Another possibility is that the path that is followed is the one that takes the least time. More experiments will be required to establish whether this is true or false. These are mathematical experiments that we suggest you do physically. Some students in the class may complain that this is somewhat repetitive and boring. If so, you can always challenge them to produce a mathematical model (a computed model) that carries out the repetitive tasks for them. In any case, students need to systematically try out a number of paths and then to find the trip time for the light in travelling from source to detector.

The path will typically consist of two segments, both in air, so you need a pair of identical rulers. Both rulers convert distance to time for light as it passes through air, so both will have identical gradations. Use one ruler for the incident path and one for the reflected path. The trip time will be the sum of the times marked on the two rulers for the path that is explored. Students should explore a number of paths and then look for something special about the path that seems most similar to the one they saw on the laboratory bench. At this stage it may be useful to have a reflected beam set up in one corner of the laboratory to remind students what they are comparing their experiment with. You might find it appropriate to encourage your students to plot a graph, showing the variation in trip time with some systematic variation in the path explored. One such possible variable, which captures the path explored, is the point at which the path hits the mirror. You might, a little light-heartedly, refer to this as a waypoint.

You might also like to arrange it so that students can easily compare the patterns they find, thereby averaging the experiment across the whole class.

You can easily extend this activity by posing questions about mirrors that are curved. Here it may be useful to have a single longer ruler that can be folded where the ruler hits the mirror

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