Don’t Accept Everything the Textbook Says

It all started one evening during the lockdown when my wife asked a simple question, ‘Why does light bend when it goes from air to glass?’

In search of an answer to this question, I looked up my son’s textbook. It simply said, ‘when a ray of light enters one transparent medium from another, it changes its path or bends at the boundary separating the two media.’ Yes. But I wondered, ‘why does light behave like this?’ Also, there was something about how the refractive index changes between different media, and how this refractive index was used to calculate how much light slows down, for example, when light enters the water from the air. Now we started wondering, ‘how is the bending of light connected to the slowing down?’ Apparently, Snell’s law and the definition of refractive index together explain the bending of light, but I was not convinced by this explanation.

So looking up the online sources, we came across this video by Bozeman Science — Refraction of Light. In this video, Paul Andersen explained the bending of light using an analogy of a Marching Band. It didn’t exactly explain why light bends, but it helped us understand what happens. So light slows down in the water when entering from the air and this slowing down makes it bend just like the Marching Band turns when going from road to sand. Paul also sneaked in another assumption that each trumpeter in the Marching Band keeps the same distance from each other, as though they were holding a stick of a fixed length, which they wouldn’t let go of. This was a good analogy and a nice way of explaining.

We went about trying to figure out using graph paper, a pen, and a pencil and saw that, ‘Yes. It does bend the way Paul explained. That was a good way to connect the light speed and the bending”. This is a neat exercise for anyone to do with a pencil, paper and a ruler and of course, an eraser.

However, some questions were still lingering!

"Why should light behave like a Marching Band? In the Marching Band, the trumpeters keep the same distance from each other. Why should the photons in the light ray keep the same distance from each other?"

This was still puzzling. Is there another law that we are missing or something?

To answer this question, we (my kids aged 15 and 13 and I) went searching online again. This time I found this video by Science Asylum. First of all, I should say, we really enjoyed the way this video was put together by them and delivered by Nick. And Science Asylum had the same problem that we had about the Marching Band analogy. Just like us, they too thought it just wasn’t convincing enough! Then, the drone and drone-clone analogy just clinched it for us! Special Thanks to Nick and Science Asylum for coming up with this analogy. It was just a wonderful simple explanation of another law called Fermat’s Principle of Least Time. Okay, now we have the refractive index of the different media, and the Fermat’s Principle of Least Time, which together explain the bending of light. Ideally, our search should have ended here, but…

The equations that were used in this video, along with the spinning arrows, didn’t quite make complete sense to me, they intrigued me and pulled me in! I vaguely recollected some physics that I learnt, probably during my B.Tech. So, as pointed out, very aptly, by Nick in the video, I had to look through their other video on how the mirror and reflection works!

Here I would like to take a slight diversion and point out another problem with textbooks.

They are not so good, generally, in connecting topics across Chapters or Grades! Somehow, students need to do this themselves. But the real problem is that there is generally no attempt to guide students to do activities to connect the different topics especially from earlier grades or even in the same grade. Some textbooks have started using a mindmap activity to do this and a mind map is a really good way for the students to connect topics in the same grade or with topics from an earlier grade.

So back from the diversion! From the Science Asylum video on mirrors and reflection, I realized that reflection is easier explained using the idea of probability and it is convincing enough with the example of the mirror with no middle surface.

But seeing Richard Feynman’s name mentioned in the references in the Asylum, I had to check out what he had said about this principle according to Quantum Electrodynamics. Then, searching online again for his lectures and watching these (Here is the link), I was really intrigued at the way he explained in such elegant terms how reflection of light is explained in the quantum world. Feynman’s explanation was truly convincing for me. So, you can do your own research and find out why!