# Homework Help: Small angle approx. optics

1. Aug 8, 2013

### Gauss M.D.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I managed to find a ratio of tangents for the two angles. From there, it seems you're supposed to go "well tan(x) ≈ x for small angles so let's magically assume this is a small angle and go grab a donut".

Why is the small angle approximation appropriate for this problem and how do I avoid getting stuck on similar problems in the future?

2. Aug 8, 2013

### Staff: Mentor

You could try a range of small angles and judge for yourself, e.g.,

x=1°: x=..... radians, sin x=....., tan x=.....

x=2°: x=..... radians, sin x=....., tan x=.....

x=3°:

By working this out for yourself, you'll be left with a better appreciation of the result.

Remember, the trig approximations expect x to be in radians.

3. Aug 8, 2013

### technician

Do what nascent oxygen recommends.....you will be surprised how 'BIG' the angle can be yet still be considered 'SMALL'

4. Aug 8, 2013

### Integral

Staff Emeritus
Of course the small angle approximation only works if you use radians.

5. Aug 8, 2013

### technician

As recommended !

6. Aug 8, 2013

### Gauss M.D.

No, I get the small angle approximation, I just don't get how I am supposed to know that it is applicable here. I mean, we're not given any angles. We're supposed to figure it out through trig/geometry trickery.Theoretically, the angles could be pi/2 for all I know.