Solving equation

[freek_g]

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 n_B. I'm trying to solve the equation conceptually.

Some comments:

• I have to solve eq (3) for n_B
• 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.

 

[Dr.Peterson]

To clarify, is your goal to eliminate s₁, so you get n_B in terms of n_A, f, and R only?

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

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[freek_g]

To clarify, is your goal to eliminate s₁, so you get n_B in terms of n_A, 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 the 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...

www.freemathhelp.com

Yes, n_A, f and R are known.

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



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

Thanks in advance

 

[Dr.Peterson]

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 ...

 

[freek_g]

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!