Question

Does your bathroom mirror show you older or younger than your actual age? Compute an order of magnitude estimate for the age difference, based on data you specify.

Answer 1

Answer on Question 52213, Physics, Optics

Question:

Does your bathroom mirror show you older or younger then your actual age? Compute an order of magnitude estimate for the age difference, based on data that you specify.

Solution:

If you stand, for example, 40cm in front of the mirror, the time required for light scattered from your face to travel to the mirror and back to your eye is:

$$\Delta t = \frac{2d}{c} = \frac{2 \cdot 0.4m}{3 \cdot 10^{8} \, m/s} = 2.67 \cdot 10^{-9} \, s.$$

Therefore, to the nearest order of magnitude, you look younger by $10^{-9} \, s$.

Answer:

The image you observe shows you $10^{-9} \, s$ younger than your current age.

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