Can the reflection of a candle appear brighter than the candle itself?

We set a candle down on a table, and next to it, a reflecting curved surface.

The light from the candle flame is of course, dispersing, spreading out and hence the apparent brightness is dropping as the distance (from our eye to the flame) squared.

The image in the mirror however is presumably made up of the parallel light rays, those reflected at the exact angle to reach our eye. It seems the apparent brightness of the reflected image should be independent of distance. (It will, of course, depend on the distance from the candle to the surface, but let's assume that's small)

Here is a rough diagram mapping this out:

Thus as we move away, is there not some point beyond which the reflection appears brighter?

Going further, could we not go an infinite distance away and the reflection still appear bright?

I'm very interested to hear the practical limitations here (such as the attainable quality of a reflective surface) but also whether the pure thought experiment holds up.

• No the thought experiment is set up wrong. When you postulate "The image in the mirror however is presumably made up of the parallel light rays", this is entirely wrong. The rays towards the mirror disperse just as much as the direct ray. In fact, assuming you had a perfect mirror and could not see the extents of it, there is no way you would ever tell if you are looking directly at a candle or a reflection of it. Jan 11, 2018 at 11:40
• This is a great point, I've updated the question slightly and changed the image to better reflect my real query. For a curved reflecting surface, it seems now to be possible for the reflected light rays to be parallel, yes? Jan 11, 2018 at 11:57
• No, you cannot do that either. This is because of Conservation Of Étendue. Relevant xkcd what-if: Fire From Moonlight. In brief: you cannot parallelize the rays, even with a curved mirror. Jan 11, 2018 at 12:06
• @a25bedc5-3d09-41b8-82fb-ea6c353d75ae, if that is the case, then it is possible to parallelize any of the rays from two separate sources? I assume not. Jan 11, 2018 at 12:17
• @Zephyr Ok, I just realized I am dead wrong. Yes you can make it so that the reflection is brighter, at least in a particular direction. This is what parabolic reflectors do. This assumes that 1) the light source is a point 2) you do not care that the image arrives distorted (but a point is a point, not a full image 3) it only works in a particular direction. In all other directions the reflection is much dimmer. Jan 11, 2018 at 12:17

Edit applied - the question has change from a flat mirror to a curved mirror. Original answer below.

With a concave mirror surface it would in principle be possible to generate some parallel rays of light from the candle that would be brighter than the candle for a longer distance, however, there are some practical difficulties.

The size of the candle is finite so the light comes from a volume rather than a fixed point, which makes generating really parrallel rays from all parts of the candle impossible. In reality what would happen is that over distance the focussed light intensity would slowly drop.

Original answer for flat mirror - or at least the original image had a flat mirror

If the candle flame is symmetrical then the path to the eye which includes mirror reflection will always be longer and so the light will always be more dispersed in the case of the mirror as it has passed over a longer distance....

There are a couple of other things to consider...

• The fraction of light reflected by the mirror will not be 100%, though it may be close to 100%

• If the mirror is in any way curved and non-parallel then the light from the candle might be brighter for a certain range of distances if the mirror focuses light from the candle somewhere in the direction of the eye and close to the eye.

In London a building, nicknamed the 'walkie talkie' has curved windows which one day focussed sunlight enough to damage a couple of cars and started a carpet to smoulder (burn with low intensity) in a shop. The building was not a perfect reflector by any means or the correct geometry to really focus the suns rays, just somewhat curved and curved enough to focus the sunlight enough to do the damage

light is in a form of light energy,so there will not be make up of light from nothing.The experiment is only collecting the light from other direction to one,not making it brighter.Infact,the four light Ray will only convert to a significant point,and at that pt you won't say the candle is brighter.Its only an image of the candle.

• Tough the OP probably mean brighter than the direct image. Jan 12, 2018 at 14:15