MadSci Network: Physics

Re: Why does the suns reflection turn square to round with greater distance?

Date: Tue Jun 12 16:36:53 2001
Posted By: Harry Adam, Research Associate, Research Division, Kodak Limited
Area of science: Physics
ID: 990309187.Ph

Hello Francisco – thank you for a good question, which is well observed on 
your part. Last year, here in England, we had a complete solar eclipse, 
and I used a mirror at the end of my garden to project a football (soccer) 
sized image of the sun on an indoor wall of the house through a window. It 
worked beautifully – so much so that I have some photographs of the 
partially eclipsed sun to show for it. As the eclipse progressed, the room 
darkened, so the image contrast remained good. Unfortunately, right at 
full eclipse, a lone cloud drifted across the sun. C’est la vie!

Anyhow – I remember thinking about the same question – I was using a 
circular mirror – no more than two inches in diameter, and wondered if the 
circle I saw was the sun or the mirror. A quick check with a square mirror 
told me it was the sun.

My first thought in answering your question was to suggest that on a sunny 
day, there is a lot of light falling on the mirror from the sky, as well 
as the direct light from the sun. When close to the wall, this reflected 
light, gathered from a fairly wide angle, is collected on the wall in a 
fairly small area and is therefore quite bright. Bright enough, maybe to 
cause the small image of the sun to be difficult to see. Although the sun 
is much brighter than the surrounding sky, it is also much smaller, and so 
the total number of lumens reflected on the wall by the sun vs the sky may 
be similar. Moving the mirror further away from the wall causes the image 
to get larger but less intense, and perhaps the larger image of the sun 
becomes better differentiated at lower overall intensity against the now 
very dim larger area of light due to reflections from the sky.  A 
photographic light meter, with some neutral density filtration (to avoid 
saturation) may be a useful tool in an experiment to investigate this.

However, there is another reason, which my colleague and friend, Gareth 
Evans, (another Mad Scientist) pointed out to me. If you take a lens (and 
a SLR camera standard lens of about 50mm focal length is a good choice) 
and open up to full aperture, you should easily be able to produce an 
image of a light source on a piece of paper. We tried it with an indoor 
light. If you make an aperture by cutting a patterned hole (say a star) in 
a piece of paper and put this over the lens when the image is sharp – it 
merely dims the image. The shape of the aperture has no effect. However, 
now move the lens close to the paper and the image goes out of focus, and 
quickly you see  patch of light the same shape as the aperture.

Taking this analogy – how does it apply to the mirror? Well we can 
consider the mirror to be a lens of infinite focal length. The light 
source – i.e. the sun - is infinitely far away (in practical terms)  and 
will be imaged out of focus when the mirror is close to the wall. Just 
like the aperture, you see an image of the mirror’s shape. Moving further 
away, the sun becomes more in focus and so you see the image of the light 
source. No, you are probably not imagining things when you observe the sun 
to be in focus.

I may not have provided you with a scientifically definitive answer here, 
but hopefully got you on the right track, and especially I hope I’ve 
prompted you to do more experiments. Therein lies the fun and excitement. 
Good luck!

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