How Do You Calculate the Angle of Reflection in Optics Problems?

[parcerita]

I have an assignment to due and it asks for the angle of reflection, but I don't know how to get it. This is the question:

"A beam of light is directed on the flat surface of a block of fused quartz (n=1.92). Part of the beam is refracted with an angle of refraction of 30°. What is the angle of reflection?"

The answer is 46.9°. What's the procedure? Thanks.

Hint: It is assumed that if it doesn't specify what medium the light is coming from then it is air (n=1.00).

 

[Doc Al]

Look up Snell's law of refraction and the Law of reflection. You'll need them both.

 

[parcerita]

Doc Al, I know Snell's Law and the law of reflection, but still can figure how to get the angle of reflection. I asked this with knowledge on the topic so your answer didn't help whatsoever.

 

[Doc Al]

Doc Al, I know Snell's Law and the law of reflection, but still can figure how to get the angle of reflection. I asked this with knowledge on the topic so your answer didn't help whatsoever.

Snell's law and the law of reflection are all you need to solve this kind of problem. Unless you show what you've done, there's no way to tell what you know and don't know.

"A beam of light is directed on the flat surface of a block of fused quartz (n=1.92).

That value for the index of refraction of fused quartz is incorrect.

 

[parcerita]

The index of refraction is not meant to be correct, it probably just made up. With Snell's Law I was able to find the angle of incidence, but I don't know what to do next. Also I thought the angle of refraction had to be at least 90° for there to be reflection, that's why I'm stuck.

 

[Doc Al]

The index of refraction is not meant to be correct, it probably just made up.

If you use the correct value, you'll quickly get the stated answer.

With Snell's Law I was able to find the angle of incidence, but I don't know what to do next.

Use the law of reflection to find the angle of reflection (this step is trivial). But you won't get the given answer without correcting the index of refraction.

Also I thought the angle of refraction had to be at least 90° for there to be reflection, that's why I'm stuck.

No. Perhaps you are confusing this with total internal reflection.

 

[parcerita]

Yeah, you are right that's total internal reflection. I can't change the index of refraction because it's a question in the assignment. It's kind of like it is what it is because the question was written that way (hope you know what I mean). Anyway thanks for trying to help ;)

 

[Doc Al]

I can't change the index of refraction because it's a question in the assignment. It's kind of like it is what it is because the question was written that way (hope you know what I mean). Anyway thanks for trying to help ;)

If you found the angle of incidence using Snell's law, then you have the angle of reflection (as described above). It just won't agree with the given answer, for the reasons stated.

Just for fun: Look up the index of refraction of fused quartz.

 

[parcerita]

Well ends up that the answer my teacher provided was wrong and that my initial answer of 74° was indeed correct. Again thanks for your help.

 

[Doc Al]

Well ends up that the answer my teacher provided was wrong and that my initial answer of 74° was indeed correct.

That's the correct answer using the information given in the problem.

But if you look up the index of refraction for fused quartz, you'll get something like n = 1.46. Use that corrected value and you'll get an answer of 46.9°.