Solving Geometry Problem: Disparity in Terms of a, D, d, e, & f

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Homework Help Overview

The problem involves finding the disparity, defined as δ = α - β, in terms of interocular distance a, viewing distance D, and variables d, e, and f. The context is rooted in geometry and trigonometric relationships.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of tangent relations to express angles α and β in terms of the given distances. There is an exploration of how to derive these angles from the geometric setup.

Discussion Status

Some participants have provided expressions for α and β, indicating progress in the discussion. However, there is no explicit consensus on the final form of δ, and the conversation remains open to further exploration.

Contextual Notes

Participants are working within the constraints of the problem statement and are attempting to clarify the relationships between the variables involved. There is an acknowledgment of the need to derive δ accurately based on the definitions provided.

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Homework Statement


Disparity is defined as \delta = \alpha - \beta. Find \delta in terms of interocular distance a, viewing distance D and d, e and f.

http://img220.imageshack.us/img220/7576/43519392.jpg

The Attempt at a Solution



I'm not getting anywhere. Any tips to get me started?
 
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I would start by writing down the tangent relations. For example, α is the difference between the two angles that Q and P make from the vertical (forward?) direction. So

α = atan(f/(D+d)) - atan(e/D)

and so forth.

BBB
 
Thanks. Then:

\beta = \arctan(\frac{a - e}{D}) - \arctan(\frac{a - f}{D + d})

Correct? Then I already have my answer it seems.
 
Yes. It seems like you're about there. Don't forget the problem asks for δ=α-β.
 

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