## Optics B/C

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

Hey I have a question:
Suppose the density of air in the atmosphere can be approximated by $log(d)=-3h/50$ where d is density in kg/m^3 and h is altitude above sea level in km. The optical depth of a column of air at some location 15 km above sea level is taken to be 1.00. Find the opacity of that column of air in m^2/kg (assume opacity is constant).

And follow up question: If the sun shines with intensity 1.300 kw/m^2 at that same location 10 km above sea level, what will its intensity be when it reaches sea level?
Okay, now that I've looked up what opacity and optical depth are, I think I have a shot at this question.

Tom_MS
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### Re: Optics B/C

Very well done! I started with the equation $dI = k*d*I*dh$, then substituted in the equation for d, brought the $I$ over to the left and integrated. Optical depth would then be equal to the negative of the resulting $ln(If/I0)$ on the left hand side. I then solved for opacity.
On the second part, I did a similar procedure except I solved for $If$ using the found value for opacity. You instead equivalently used the mean density over the column and multiplied it by the change in height. Very good! Unfortunately, I believe you miscalculated on your very last line the final answer for the second part.

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

What color has the highest deviation in a prism?

Pettywap
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### Re: Optics B/C

violet
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### Re: Optics B/C

violet

Pettywap
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### Re: Optics B/C

A pair of ideal polarizing filters are placed one in front of the other near a source of light so that the rays arrive perpendicular to the planes of the filters. What angle should the polarization axes be placed so that the second filter transmits 0.25 of the light energy it receives?
"Who's Fettywap?"

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

A pair of ideal polarizing filters are placed one in front of the other near a source of light so that the rays arrive perpendicular to the planes of the filters. What angle should the polarization axes be placed so that the second filter transmits 0.25 of the light energy it receives?

Pettywap
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### Re: Optics B/C

A pair of ideal polarizing filters are placed one in front of the other near a source of light so that the rays arrive perpendicular to the planes of the filters. What angle should the polarization axes be placed so that the second filter transmits 0.25 of the light energy it receives?
"Who's Fettywap?"

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

A converging lens in air is placed underwater. What happens to the lens?

Hint: Be careful.

chopchpp
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### Re: Optics B/C

A converging lens in air is placed underwater. What happens to the lens?

Hint: Be careful.
focal length increases?

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

A converging lens in air is placed underwater. What happens to the lens?

Hint: Be careful.
focal length increases?
There's more to the correct answer.

Hint 2: I didn't specify what the lens was made out of.

Pettywap
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### Re: Optics B/C

A converging lens in air is placed underwater. What happens to the lens?

Hint: Be careful.
focal length increases?
There's more to the correct answer.

Hint 2: I didn't specify what the lens was made out of.
It also depends on the index of refraction of the lens. The focal length could be infinity because the converging lens could be the same material as water, which means there is no refraction.
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UTF-8 U+6211 U+662F
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### Re: Optics B/C

Almost there, a little more to the answer.

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### Re: Optics B/C

All right, my question killed the marathon, so I'll just post the answer.
1) Fill in the blank: Stars moving toward us appear more _ (color).
2) Why is this?

jonboyage
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### Re: Optics B/C

All right, my question killed the marathon, so I'll just post the answer.
1) Fill in the blank: Stars moving toward us appear more _ (color).
2) Why is this?
Blue; wavelength decreases due to Doppler shift
I was in a bin

Rustin '19
UPenn '23