/sci/ - Science & Math » Thread #11757953

99KiB, 738x980, derrivation.png

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Anonymous Wed 03 Jun 15:12:27 2020 No.11757953 View Reply Original Report

Quoted By: >>11758023 >>11758052 >>11758124

How the fuck do I do this derivation from (4) to (5). I didn't think I was a brainlet but apparently I am. Any trig bros wanna help me out?

Anonymous

View Same Google iqdb SauceNAO 5-1-fundamental-trig-identities-n.jpg, 50KiB, 720x540

Anonymous Wed 03 Jun 2020 15:41:59 No.11758023 Report

Quoted By: >>11758062 >>11758142 >>11758161

>>11757953
I too am brainlet but I believe the answer lies in (pic I posted).

Anonymous

Anonymous Wed 03 Jun 2020 15:45:01 No.11758031 Report

Quoted By:

Physics is so fucking ugly lmao

Anonymous

Anonymous Wed 03 Jun 2020 15:54:04 No.11758052 Report

Quoted By: >>11758062

>>11757953
Equation (4) is dependent on phi_2, equation (5) is not. There is no relation established between phi_2 and alpha and beta. They are therefore not equivalent.

Anonymous

Anonymous Wed 03 Jun 2020 16:03:15 No.11758062 Report

Quoted By: >>11758109

>>11758023
Already been looking at these, definitely related but I can't figure out how to get rid of these damn cos terms in eq(4)

>>11758052
I think that's where the sine condition comes in, but I'm not sure how to use it in this context. Possibly
sin alpha/ sin phi_1 = sin beta/sin phi_2
Either way they are definitely equivalent.

Anonymous

Anonymous Wed 03 Jun 2020 16:32:32 No.11758109 Report

Quoted By: >>11758111

>>11758062
>I think that's where the sine condition comes in
This is nowhere specified. In fact, the picture does not define what the "sine condition" is. Given the equations in the image, (4) and (5) are not equivalent. Perhaps there is additional information earlier in the book.

Anonymous

Anonymous Wed 03 Jun 2020 16:33:23 No.11758111 Report

Quoted By: >>11758149

>>11758109
"We now assume that the objective lens obeys the sine condition"

https://en.wikipedia.org/wiki/Abbe_sine_condition#:~:text=The%20Abbe%20sine%20condition%20is,in%20the%20context%20of%20microscopes.

Anonymous

Anonymous Wed 03 Jun 2020 16:37:08 No.11758124 Report

Quoted By:

>>11757953
it's just some middle school algebra bro xD

seriously though this is the fucking problem with like every engineering and physics textbook ever written

Anonymous

Anonymous Wed 03 Jun 2020 16:43:49 No.11758142 Report

Quoted By:

>>11758023
the identities you want are probably the double angle formulas.

cos(2A) = cos^2(A)-sin^2(A)
or
cos(2A) = 1-2sin^2(A)

will allow you to eliminate the cos

Anonymous

Anonymous Wed 03 Jun 2020 16:48:18 No.11758149 Report

Quoted By: >>11758161

>>11758111
Strange, from that I get that (5) is equivalent to (4) except the first cos is a sin.

Anonymous

Anonymous Wed 03 Jun 2020 16:53:48 No.11758161 Report

Quoted By: >>11758167

>>11758149
Oh nevermind, I was just sloppy. It checks out. Just use Abbe under the radical as well as the very first Pythagorean identity here:
>>11758023

[spoiler:lit]I still think physics is fucking ugly though[/spoiler:lit]

Anonymous

Anonymous Wed 03 Jun 2020 16:56:16 No.11758167 Report

Quoted By: >>11758176

>>11758161
Yeah I just figured it out too, forgot I could do cos^2 = 1 - sin^2

fell into place after that

Anonymous

Anonymous Wed 03 Jun 2020 16:58:39 No.11758176 Report

Quoted By: >>11758179

>>11758167
>physicists

Anonymous

Anonymous Wed 03 Jun 2020 17:02:03 No.11758179 Report

Quoted By: >>11758271

>>11758176
I haven't used trig identities in like 10 years, ever since I found out you could just convert trigs into exponentials I just did that, makes it 100x easier to rearrange.

Anonymous

Anonymous Wed 03 Jun 2020 17:46:53 No.11758271 Report

Quoted By:

>>11758179
don't mind him. this is how you learn

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