Optics B/C

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

Postby UTF-8 U+6211 U+662F » February 8th, 2018, 5:48 pm

Hey I have a question:
Suppose the density of air in the atmosphere can be approximated by 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.
Point of confusion: The equation given for density doesn't make sense dimensionally, so I'll modify the equation to log(d * 1 m^3/kg) = 3h/50 km. opacity (in m^2/kg) = attenuation coefficient (in m^-1) / density (in kg/m^3) density (in kg/m^3) = 10^(-3h/50 km) * 1 kg/m^3 attenuation coefficient (in m^-1) = opacity (in m^2/kg) * 10^(-3h/50 km) * 1 kg/m^3 1 = [math]\int_{0 km}^{15 km} \textrm{attenuation coefficient} (m^{-1}) dh = \textrm{opacity} (\frac{m^2}{kg}) * 1 \frac{kg}{m^3} * \int_{0 km}^{15 km} 10^(\frac{-3h}{50 km}) dh[/math] = according to WolframAlpha, 6.327 kgkm/m^3 * opacity (in m^2/kg) = 6327 kg/m^2 * opacity (in m^2/kg) 1 = 6327 kg/m^2 * opacity (in m^2/kg) opacity = 1/(6327 kg/m^2) = [b]0.000158 m^2/kg[/b] I = 1.300 kW/m^2 * exp(-0.000158 m^2/kg * density * 10000 m). Let's use the value .542 kg/m^3 for density (mean of all of the densities between 0 km and 10 km) = 1.300 kW/m^2 * exp(-0.000158 m^2/kg * .542 kg/m^3 * 10000 m) = [b]0.657 kW/m^2[/b] Not sure what I just did.

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Re: Optics B/C

Postby Tom_MS » February 9th, 2018, 8:33 am

Very well done! I started with the equation , then substituted in the equation for d, brought the over to the left and integrated. Optical depth would then be equal to the negative of the resulting on the left hand side. I then solved for opacity.
On the second part, I did a similar procedure except I solved for 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.

Alright, your turn!

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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 9th, 2018, 4:19 pm

What color has the highest deviation in a prism?

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Re: Optics B/C

Postby Pettywap » February 9th, 2018, 6:53 pm

violet
"Who's Fettywap?"

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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 10th, 2018, 11:02 am

violet
Good, your turn.

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Re: Optics B/C

Postby Pettywap » February 11th, 2018, 4:28 am

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?
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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 11th, 2018, 9:10 am

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?
Answer
[math]\cos^2 \theta = \frac14; \cos \theta = \frac12; \theta = \frac\pi3 = 60 \degree.[/math]

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Re: Optics B/C

Postby Pettywap » February 11th, 2018, 3:07 pm

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?
Answer
[math]\cos^2 \theta = \frac14; \cos \theta = \frac12; \theta = \frac\pi3 = 60 \degree.[/math]
Correct!! your turn
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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 11th, 2018, 3:44 pm

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

Hint: Be careful.

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Re: Optics B/C

Postby chopchpp » February 11th, 2018, 4:33 pm

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

Hint: Be careful.
focal length increases?

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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 11th, 2018, 4:47 pm

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.

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Re: Optics B/C

Postby Pettywap » February 11th, 2018, 6:19 pm

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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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 11th, 2018, 6:24 pm

Almost there, a little more to the answer.

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Re: Optics B/C

Postby UTF-8 U+6211 U+662F » February 19th, 2018, 10:05 am

All right, my question killed the marathon, so I'll just post the answer.
Answer
If the refractive index of the lens > 1.33: The focal length increases. If the refractive index of the lens = 1.33: The lens becomes invisible. If the refractive index of the lens < 1.33: The lens becomes diverging.
1) Fill in the blank: Stars moving toward us appear more _ (color).
2) Why is this?

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Re: Optics B/C

Postby jonboyage » February 19th, 2018, 10:48 am

All right, my question killed the marathon, so I'll just post the answer.
Answer
If the refractive index of the lens > 1.33: The focal length increases. If the refractive index of the lens = 1.33: The lens becomes invisible. If the refractive index of the lens < 1.33: The lens becomes diverging.
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

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