How Is the Sun's Angle of Inclination Calculated from Underwater?

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Homework Help Overview

The discussion revolves around calculating the Sun's angle of inclination as observed by a scuba diver underwater, given an apparent angle and the refractive index of water. The problem involves concepts of optics and refraction.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculations involving the refractive index and the apparent angle of the Sun. Questions arise regarding whether the angle of inclination should be measured from the vertical or the horizontal, leading to differing interpretations of the problem's requirements.

Discussion Status

There is ongoing exploration of the correct interpretation of the angle measurement. Some participants express confidence in the calculations, while others highlight potential ambiguities in the problem statement. Guidance has been offered regarding the significance of angle measurement in relation to the water surface.

Contextual Notes

Participants note that the problem is part of an online system, which may have specific requirements regarding significant figures. There is also mention of verifying the problem setup with a professor.

akmphy
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Angle of Inclination: ?

Homework Statement


An underwater scuba diver sees the Sun at an apparent angle of 23 degrees from the vertical. The refraction index for water is 1.32. what is the Sun's angle of inclination?


Homework Equations


n1sin(degree)= n2sin(degree)


The Attempt at a Solution


1.32sin(23) = 1sin(degree)
sin-1 (.51576) = 31.04
This was the wrong answer. I thought this was straightforward. I must be missing something here.
 
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Your work looks fine to me. Are you sure they want the Sun's angle of inclination from the vertical?
 


The problem asks for the Sun's angle of inclination?
wouldn't that be the angle it strikes the surface of the water?
 


akmphy said:
The problem asks for the Sun's angle of inclination?
wouldn't that be the angle it strikes the surface of the water?
That's what I would say. Measured from the horizontal, not the vertical.
 


So, I tried that...
90-31.05 = 58.95
This was wrong as well.
 


If this is an online system, they can be picky about significant figures.

(If it's from a textbook, tell me which one and what problem.)
 


It is an online UT program. Do you think the set up is correct? I will e-mail professor to double check.
 


As I said, your work looks fine to me. The only ambiguity is whether the inclination of the Sun is with respect to the horizontal or not. But that doesn't explain your experience with the online system.
 


I wish I was more savvy with the computer. The angle desired is with respect to the horizontal...the water surface.
However, it must be a glitch. That would be 90-31.05, which was wrong.
Thanks for your help
 

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