Optics B/C

Test your knowledge of various Science Olympiad events.
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Avogadro
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Re: Optics B/C

Post by Avogadro » February 26th, 2017, 3:20 pm

UTF-8 U+6211 U+662F wrote:
If 700 nm is red and 450 nm is blue, then green?
Correct! Your turn/
Lower Merion 2017
Subtitled: Revenge of the Non-Harriton

Placement Record:

Code: Islip | Conestoga | Tiger | Regionals | States
Out of: 61 | 42 | 36 | 37 | 36

Chemistry Lab: 9 | - | - | 4 | 4
Astronomy: 14 | - | 5 | 10 | 3
Material Science: 12 | 19 | 9 | 5 | 9
Optics: 14 | 7 | 3 | 4 | 2

UTF-8 U+6211 U+662F
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Re: Optics B/C

Post by UTF-8 U+6211 U+662F » February 27th, 2017, 4:29 pm

A laser is pointed at mirror A with an angle of incidence of 50 degrees. Mirror A is connected to Mirror B at a 30 degree angle. What is the angle of reflection off of mirror B?

(The mirrors look something like this:

Mirror A
<
Mirror B

)

Avogadro
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Re: Optics B/C

Post by Avogadro » March 2nd, 2017, 6:23 pm

UTF-8 U+6211 U+662F wrote:A laser is pointed at mirror A with an angle of incidence of 50 degrees. Mirror A is connected to Mirror B at a 30 degree angle. What is the angle of reflection off of mirror B?

(The mirrors look something like this:

Mirror A
<
Mirror B

)
20°?
Lower Merion 2017
Subtitled: Revenge of the Non-Harriton

Placement Record:

Code: Islip | Conestoga | Tiger | Regionals | States
Out of: 61 | 42 | 36 | 37 | 36

Chemistry Lab: 9 | - | - | 4 | 4
Astronomy: 14 | - | 5 | 10 | 3
Material Science: 12 | 19 | 9 | 5 | 9
Optics: 14 | 7 | 3 | 4 | 2

UTF-8 U+6211 U+662F
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Re: Optics B/C

Post by UTF-8 U+6211 U+662F » March 3rd, 2017, 6:10 pm

That's what I got, yep!

Avogadro
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Re: Optics B/C

Post by Avogadro » March 4th, 2017, 6:47 am

Cool.

A beam of light enters a prism with an index of refraction of 1.35. If each of the angles of the prism is 60°, what maximum angle must the angle of incidence be so that no light comes out the other side?
Lower Merion 2017
Subtitled: Revenge of the Non-Harriton

Placement Record:

Code: Islip | Conestoga | Tiger | Regionals | States
Out of: 61 | 42 | 36 | 37 | 36

Chemistry Lab: 9 | - | - | 4 | 4
Astronomy: 14 | - | 5 | 10 | 3
Material Science: 12 | 19 | 9 | 5 | 9
Optics: 14 | 7 | 3 | 4 | 2

UTF-8 U+6211 U+662F
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Re: Optics B/C

Post by UTF-8 U+6211 U+662F » March 5th, 2017, 10:03 am

Avogadro wrote:Cool.

A beam of light enters a prism with an index of refraction of 1.35. If each of the angles of the prism is 60°, what maximum angle must the angle of incidence be so that no light comes out the other side?
Assuming a surrounding index of refraction of 1, arcsin(1/1.35) = 47.8 deg, which requires an angle of refraction of 77.8 deg, so 1*sin(theta) = 1.35*sin(77.8 deg), theta = arcsin(1.35*sin(77.8 deg)), and theta = undefined. Therefore, light always comes out the other side?

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Re: Optics B/C

Post by Avogadro » March 7th, 2017, 7:58 am

UTF-8 U+6211 U+662F wrote:
Avogadro wrote:Cool.

A beam of light enters a prism with an index of refraction of 1.35. If each of the angles of the prism is 60°, what maximum angle must the angle of incidence be so that no light comes out the other side?
Assuming a surrounding index of refraction of 1, arcsin(1/1.35) = 47.8 deg, which requires an angle of refraction of 77.8 deg, so 1*sin(theta) = 1.35*sin(77.8 deg), theta = arcsin(1.35*sin(77.8 deg)), and theta = undefined. Therefore, light always comes out the other side?
Yeah, looks like I accidentally made a trick question lol. Good practice anyway! :P
Lower Merion 2017
Subtitled: Revenge of the Non-Harriton

Placement Record:

Code: Islip | Conestoga | Tiger | Regionals | States
Out of: 61 | 42 | 36 | 37 | 36

Chemistry Lab: 9 | - | - | 4 | 4
Astronomy: 14 | - | 5 | 10 | 3
Material Science: 12 | 19 | 9 | 5 | 9
Optics: 14 | 7 | 3 | 4 | 2

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Re: Optics B/C

Post by Tom_MS » March 8th, 2017, 11:37 am

Avogadro wrote:
UTF-8 U+6211 U+662F wrote:
Avogadro wrote:Cool.

A beam of light enters a prism with an index of refraction of 1.35. If each of the angles of the prism is 60°, what maximum angle must the angle of incidence be so that no light comes out the other side?
Assuming a surrounding index of refraction of 1, arcsin(1/1.35) = 47.8 deg, which requires an angle of refraction of 77.8 deg, so 1*sin(theta) = 1.35*sin(77.8 deg), theta = arcsin(1.35*sin(77.8 deg)), and theta = undefined. Therefore, light always comes out the other side?
Yeah, looks like I accidentally made a trick question lol. Good practice anyway! :P
It looks like you just used snell's law and the critical angle and didn't use the 60 degree apex angle. Using geometry (which is kind of complicated to explain here), I'm getting the formula of theta=arcsin( n*sin( 60 - arcsin(1/n))). This gives be 16.58 degrees. If this angle was decreased (I think) any more, no light would escape.

UTF-8 U+6211 U+662F
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Re: Optics B/C

Post by UTF-8 U+6211 U+662F » March 8th, 2017, 12:54 pm

Tom_MS wrote:
Avogadro wrote:
UTF-8 U+6211 U+662F wrote:
Assuming a surrounding index of refraction of 1, arcsin(1/1.35) = 47.8 deg, which requires an angle of refraction of 77.8 deg, so 1*sin(theta) = 1.35*sin(77.8 deg), theta = arcsin(1.35*sin(77.8 deg)), and theta = undefined. Therefore, light always comes out the other side?
Yeah, looks like I accidentally made a trick question lol. Good practice anyway! :P
It looks like you just used snell's law and the critical angle and didn't use the 60 degree apex angle. Using geometry (which is kind of complicated to explain here), I'm getting the formula of theta=arcsin( n*sin( 60 - arcsin(1/n))). This gives be 16.58 degrees. If this angle was decreased (I think) any more, no light would escape.
the angle of 77.8 deg
Anyways new question:
A Science Olympiad Optics supervisor holds up two white flashlights. The first has a magenta filter, and the second has a cyan filter. What color is the overlap of the two flashlights?

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Re: Optics B/C

Post by jonboyage » March 8th, 2017, 2:12 pm

UTF-8 U+6211 U+662F wrote:
Tom_MS wrote:
Avogadro wrote: Yeah, looks like I accidentally made a trick question lol. Good practice anyway! :P
It looks like you just used snell's law and the critical angle and didn't use the 60 degree apex angle. Using geometry (which is kind of complicated to explain here), I'm getting the formula of theta=arcsin( n*sin( 60 - arcsin(1/n))). This gives be 16.58 degrees. If this angle was decreased (I think) any more, no light would escape.
the angle of 77.8 deg
Anyways new question:
A Science Olympiad Optics supervisor holds up two white flashlights. The first has a magenta filter, and the second has a cyan filter. What color is the overlap of the two flashlights?
I'm getting the same exact answer of 16.5836 degrees and I made sure it was right by doing it the long way and going through each step that leads to the condensed formula Tom described
I'm not 100% sure about this but is it light blue?
I was in a bin

Rustin '19
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