A great engineering/physics question.

It is still very early in my teaching career and I'm not by any means reaching my own standards, but I did come up with this question that I'm proud of.

Light travels from air into some unknown medium as show in the figure.

1. Is the index of refraction larger or smaller than in air? Show a proof explaining your choice?
2. Calculate the index of refraction of the unknown medium using a protractor. Note that the index of refraction in air is 1.0003. 
3. What is the critical angle between air and the unknown material?
4. Draw an accurate path for a light beam that travels from the air into the unknown medium and reflects at least one time inside the medium.

I just finished marking this question. Most students did an excellent job of question 1. I'm proud of that. 

Question 4, however, left most of my students in the dust. In a weird way, this also makes me proud. Some students just drew an incident line inside the medium being reflected that was larger than the critical angle. Another group of students just threw their hands up and listened to the cries that there is no angle that will work. Other correctly drew pictures with an incident ray that goes into the unknown medium from the left side surface, refracts, then reflects off the top side surface. This is the correct answer, but then when they tried to get correct angles they failed and said it was  impossible. They failed because the reflected angle is much larger than the critical angle. They started their reverse engineering by stating that the reflected angle was the critical angle. Their failure I attribute to my own inaptitudes as a teacher but now I know about it. 

If you have an idea on how to improve the question please leave a comment. If you know how to help me teach the skills my students need for the fourth question that would also be helpful.

Anywho, that it is for the today. 

Mr. Samson