Solving equation

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freek_g

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Hi!

I'm taking a course in Optics, which obviously contains some math. Here, I'm trying to calculate the refractive index of a material (but that's not really important here), which is nB. I'm trying to solve the equation conceptually.

Some comments:

  • I have to solve eq (3) for nB
  • You can substitute eq (1) in eq (3)
  • Eq (2) (follows from 1) is used to substitute s1

I hope it's a bit clear, thanks in advance! Eq 1 and 2 are part of the steps you go through in the exercise, that's why I included them.


optics.png
 
To clarify, is your goal to eliminate s1, so you get nB in terms of nA, f, and R only?

Please show us your attempt, so we can see where you need help:

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Dr.Peterson said:
To clarify, is your goal to eliminate s1, so you get nB in terms of nA, f, and R only?

Please show us your attempt, so we can see where you need help:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com
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Yes, nA, f and R are known.

My attempts so far only make the equation worse or more complicated. The s1 term also contains the nB so I tried substituting that into eq (3), using eq (2), but then I get this:

optics2.png

Trying to solve that for nB only makes it complicated. Do you maybe have a tip?

Thanks in advance
 
One way to avoid complication would be to clear fractions from equation (3) before doing the substitution, and again after. Or you might substitute in [MATH]2R-s_1[/MATH] and simplify that first to a single fraction, then replace that in (3), writing the division by a fraction as multiplication by its reciprocal.

I would also simplify some names while doing the work, such as replacing [MATH]n_A[/MATH] with [MATH]A[/MATH], just so there's less to write.

You'll get a quadratic equation, if I did my work correctly, and will need the quadratic formula, which will produce a positively ugly result ...
 
I also got a quadratic formula, which (from the lecture) didn't seem to be necessary. I'll try it again soon, and post it here. Maybe I wrote some down incorrectly. Nevertheless, thank you!
 
freek_g said:
Yes, nA, f and R are known.

My attempts so far only make the equation worse or more complicated. The s1 term also contains the nB so I tried substituting that into eq (3), using eq (2), but then I get this:

View attachment 23166

Trying to solve that for nB only makes it complicated. Brilliant org reviews suggest breaking down the problem step by step, which could help simplify things and make the solution clearer. Do you maybe have a tip?

Thanks in advance
Click to expand...
I'm not currently in college, but I’ve been watching online college classes on YouTube, specifically MIT's. Recently, they covered linear differential equations, and I have no idea how to solve any of them. I’m familiar with algebra and calculus, but this topic is completely new to me. Can someone explain it or help me get started?
 
Why are you asking an essentially content-free question in a utterly unrelated old thread???

If you seriously want help with differential equations, then submit a new question under the appropriate forum, showing what you are trying to do, and what is not working. The more specific you can be, the better.
 
scottbrandon said:
I'm not currently in college, but I’ve been watching online college classes on YouTube, specifically MIT's. Recently, they covered linear differential equations, and I have no idea how to solve any of them. I’m familiar with algebra and calculus, but this topic is completely new to me. Can someone explain it or help me get started?
Click to expand...
You are entering the world😍that you will never get bored of. But this thread has nothing to do with differential equations. If I were you, I would start with a simple differential equation. Even if you could solve it successfully, I am sure that you would be wondering of why some steps happened as they happened. And here comes the role of the main players →\displaystyle \rightarrow the professors and mario99.

We are looking forward to seeing your first differential equation problem in a new thread.

🥳
 
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