Optimizing Rear-View Mirror Dimensions for Full Rear Window Visibility

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SUMMARY

The discussion focuses on calculating the minimum dimensions of a rear-view mirror to ensure full visibility of a rear window measuring 1.3 m in width and 0.30 m in height. The driver's eyes are positioned 0.62 m from the mirror and 1.58 m from the rear window. Using basic geometry, specifically the tangent function, participants aim to determine the necessary width of the mirror to capture the entire rear window without head movement. The solution involves visualizing the setup and applying geometric principles to establish the required dimensions.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly the tangent function.
  • Familiarity with visualizing geometric relationships in a three-dimensional space.
  • Knowledge of how to apply trigonometric ratios to real-world problems.
  • Ability to interpret and manipulate geometric diagrams effectively.
NEXT STEPS
  • Study the application of the tangent function in real-world scenarios.
  • Research geometric principles related to angles and line of sight.
  • Explore methods for visualizing three-dimensional objects in two-dimensional diagrams.
  • Learn about the design considerations for automotive mirrors and visibility standards.
USEFUL FOR

Automotive engineers, physics students, and anyone involved in vehicle design or safety assessments will benefit from this discussion.

yayirunin2car
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Homework Statement


The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.62 m from the driver's eyes, and 1.58 m from the rear window. What are the minimum dimensions for the rear-view mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?


Homework Equations


None really - other than regular geometry stuff like tan theta = y/x, etc.


The Attempt at a Solution


I have none, I've been trying to draw this thing and make triangles or something but I'm completely lost.

Thanks in advance for any help!
 
Physics news on Phys.org
Forget that it's a mirror and draw the rear window the correct distance in front of the driver, now draw the mirror as a slot restricting the width - how wide does it have to be to get the lines from the driver to the corners of the 'rear' mirror?
 
Yes! Thank you, :-).
 

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