Is the image upright for a reflective spherical balloon using ray tracing?

Thread starter lorenz0
Start date Feb 4, 2022
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Balloon Geometric optics Magnification Spherical Thin lens

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SUMMARY

The discussion confirms that the image produced by a reflective spherical balloon using ray tracing is upright. The equation used, ##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}##, with focal length ##f=-2## and magnification ##M=-\frac{q}{p}=\frac{3}{4}##, leads to the conclusion that the object distance ##p## is approximately 0.67 cm. This analysis is validated by the participants, establishing the correctness of the calculations.

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Feb 4, 2022

lorenz0

Homework Statement: A balloon has a fully reflective spherical surface with a diameter of ##8 cm##.
Determine the distance of an object whose reflected image appears to be reduced to ##3/4## of its real size.
Is the image upright or inverted?

Relevant Equations: ##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}##, ##f=-\frac{R}{2}##, ##M=-\frac{q}{p}##

From ray tracing I would say that the image is upright.
Using the equation ##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}## with ##f=-\frac{R}{2}=-2## and ##M=-\frac{q}{p}=\frac{3}{4}## I get ##p=\frac{2}{3}cm\simeq 0.67 cm##.

Is this correct? Thanks

Last edited: Feb 4, 2022