## Refraction and trip time

Classroom Activity for 14-16

What the Activity is for

In this activity, students get to explore possibilities to find out why a refracted 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 refracting objects
- a sharpened pencil

What Happens During this Activity

Start by performing an impressive demonstration of refraction. It might also be a good idea to remind the students how beams refract by using rectangular glass blocks 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 refraction, and the angle of incidence and one being larger than the other, should be the starting point, and not the endpoint.

#### So the puzzle is the following:

Teacher: Why does the beam follow the path that it does, as it passes from one medium to another?

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. It won't take much experimenting to show that this is false. You don't need any special rulers for this.

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 paths will typically consist of two segments: one in air, and one in a different medium. Since the apparent speed of light in these two media is different, use two different rulers. One ruler converts distance to time for light in air; the other converts distance to time for light in the other medium. 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, concentrating on the transition through a single interface between the air and the medium. At this stage it may be useful to have a refracted 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 that captures the path explored is the point at which the path passes from one medium to another. 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 using more complex shapes, which will inevitably involve three steps in calculating the trip time, as such shapes will involve two changes of medium. You might try a rectangular block and then a prism, as linked first steps.