Reflecting Astronomy!

Classical Mechanics Level 2

A ray of light enters an assembly of plane mirrors (from left) as shown in the figure below and undergoes reflection at all the four mirrors. After the last reflection, the ray travels in vertical direction and enters in the detecting instrument. In the figure, the dotted lines are normals for respective mirrors and dashed lines are exactly vertical or horizontal. The third mirror is exactly horizontal. It is known that angle $θ$ is ${50}^{◦}$ . Angle $\phi$ is unknown. Find angle $p$ .

This question appeared in INAO 2015

The answer is 10.

1 solution

Michael Mendrin
Oct 29, 2016

The first mirror is tilted 40 degrees from horizontal. Angle p therefore is 10 degrees.

Could I ask you, why does light obey the law of reflection?

Swapnil Das - 4 years, 7 months ago

Fermat's Principle states that light will follow the Path of Least Time. The interesting question is, "and so why should light want to follow a path of least time?" That's where we get into deeper physics. In Classical Mechanics, there's the Principle of Least Action. In Quantum Field Theory, Fermat's Principle of Least Time is explained in terms of "Probabilistic Sum of All Possible Paths". And in General Relativity, light follows a spacetime geodestic, which is the Path of Longest Proper Time. And then we can get into more esoteric explanations such as Principle of Maximum Entropy Production, but I'm now getting ahead of myself....

What's fun about physics is how all of these principles are actually interrelated, when you get down to the mathematics of them. These different interpretations may seem to contradict each other, but they all share the same basic underlying mathematics.

Michael Mendrin - 4 years, 7 months ago

I never expected that I'll be provided such an advanced, but still clear answer to such a simple-looking question.

Sir, do you remember from where did you study Optics? Could share the name of the source with us?

Swapnil Das - 4 years, 7 months ago

@Swapnil Das – Besides an elementary introduction to optics in undergraduate college, the first book I had on this subject, which I still have somewhere, is the Dover Publications "Introduction To Modern Optics". This pdf here is for a later edition of the same.

Introduction To Modern Optics

Michael Mendrin - 4 years, 7 months ago

@Michael Mendrin – Thanks a lot sir! I shall be indebted to you for the rest of my life :)

Swapnil Das - 4 years, 7 months ago

@Swapnil Das – Also, for an excellent easy introduction to QED (Quantum Field Theory), check out QED: The Strange Theory of Light and Matter by Richard Feynnman. You probably can order an used paperback for cheap. I highly recommend this book.

Michael Mendrin - 4 years, 7 months ago

@Michael Mendrin – I've heard that popular science books give a lot of 'meaningless and rigourless' thoughts about the subject. Is it the same for this book? I ask this because I will probably be studying the subject with serious thoughts after years.

Swapnil Das - 4 years, 7 months ago

@Swapnil Das – Richard Feynnman is a Nobel Prize winner in physics, and is widely considered to be one of the top physicists in history. He has authored many books, for laymen, students, and professionals. His book QED: The Strange Theory (etc) is a clearly written introduction to the "weird logic" of quantum field theory, and being that he is actually one of the principal developers of QED (having won the Nobel Prize for that), I would say he knows exactly what he is talking about. His other books for professionals are certainly more "rigorous", but it's a good chance you won't be able to understand them right now, as they are quite advanced. That's why he has written an introductory text for those that want to get an idea of what's going on.

Michael Mendrin - 4 years, 7 months ago

@Michael Mendrin – I must read that then. Thanks a lot!

Swapnil Das - 4 years, 7 months ago