Question

You stand 45 cm from your bathroom mirror. You scatter light which travels to the mirror and back to you. Does your bathroom mirror show you older or younger than your actual age? Use Fermat’s principle to compute an order-of-magnitude estimate for the age difference.

Answer 1

Solution

Taking account of the fact that light takes finite time to travel between two points, the bath room mirror actually shows a younger you to you. Light scatters of you and it will travel a distance (here 45cm) with some time and mirror reflect back the light again it takes that much time to come back to your eyes. So you are actually watching at yourself a tiny fraction of second younger than your actual age. Now light travels at speed 3*10^8 m/s in vacuum. It travels with almost the same speed in air also. So assuming this speed for light in air, the time taken to travel 45+45=90cm=0.9m distance by time,

Thus you will be looking at a ' you ' younger by 3 nano seconds ​​​​​​.