Case (I)
A video image of a man, carried by light, enters a spherical planet made of a transparent material with refractive index 𝜇 > 1. The light emerges from the diametrically opposite side of the planet, where it is viewed. The diameter of the planet is 𝑑.
Case (II)
The same video image is viewed after the light has travelled a distance d through vacuum.
In which case will the man appear younger to the observer?
Assume that the man continues to age normally while the light is travelling.
Answer
The key idea is that we see an object as it was when the light left it.
The light slows down in case (I) so that the observer sees the image from an earlier time. Image from an earlier time means younger man.
Mathematically, speed of light in case (I), $v=\frac {c}{𝜇}$
Time taken to cross diameter, $t= \frac {𝜇d}{c}$
In case (II), time taken to cover the same distance d in vacuum, $t'=\frac {d}{c}$
Since, 𝜇 > 1, t > t'
So, in Case (I), the light takes longer to reach the observer. Consequently, the observer sees the man as he was further back in time.
For example, Case I might show the man as he was 10 years ago. Case II might show him as he was 1 year ago.
Thus, the image in Case I corresponds to an earlier, younger version of the man.
The man appears younger in Case (I).
The important distinction is: a greater propagation delay means we see an older event, but the person depicted in that older event is younger.