Plane Mirror Optics: Determining Minimum Mirror Size for Viewing Entire Image

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SUMMARY

The discussion focuses on determining the minimum size of a plane mirror required for a person of height 1.50 m to view their entire reflection. The key conclusion is that the minimum mirror height must be half of the person's height, which is 0.75 m. Additionally, the position of the observer relative to the mirror influences the perceived image size, necessitating a clear understanding of reflection principles. A diagram is recommended to visualize the relationship between the observer's distance and the mirror's dimensions.

PREREQUISITES
  • Understanding of basic optics principles, specifically reflection.
  • Familiarity with geometric diagrams and scaling.
  • Knowledge of human anatomy related to height measurements.
  • Ability to apply mathematical reasoning to physical scenarios.
NEXT STEPS
  • Research the laws of reflection in optics.
  • Learn how to create scaled diagrams for geometric problems.
  • Explore the concept of image distance in plane mirrors.
  • Study practical applications of mirror sizes in everyday settings.
USEFUL FOR

Students studying physics, particularly those focusing on optics, as well as educators seeking to explain the principles of reflection and image formation in mirrors.

Speedking96
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Homework Statement



While you were looking at the reflection of your feet in a plane mirror,
you saw a dark spot on the glass. Assuming your height is 1.50 m, and that
the eyes are located 0.1 m below the top of the head

(a) What is the distance between the spot and the floor?

(b) What is the minimum amount of mirror needed to see your entire image?

2. The attempt at a solution

I have correctly solved part (a) using a scaled diagram; however, I am having a hard time understanding part (b). This is because, logically, wouldn't your position, relative to the mirror dictate the amount of mirror needed to see the entire image? If someone could please point me in the right direction. Thank you.
 
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Speedking96 said:
This is because, logically, wouldn't your position, relative to the mirror dictate the amount of mirror needed to see the entire image?
Draw a diagram. Hint: If you stand a distance "d" from the mirror, how far away is your image.
 

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