Last week I heard about for the first time something that is common knowledge to all women in the western world – namely that women’s clothes shops use convex mirrors to make you appear thinner. Since I don’t frequent women’s clothes shops particularly often (I don’t frequent men’s clothes shops more than is strictly necessary, either – going shopping is my idea of torture) this essential fact had escaped me.
I guess the assumption is that if you see yourself looking a little thinner than you are used to, your opinion of the clothes you are wearing is improved, and you are more likely to buy. Probably there is research to back that up, but it’s Friday afternoon and I have better things to do (like swimming) so I’m not inclined to go looking for it. (Question – does knowing that the mirror is tricking you change your assessment of the situation? – I bet there’s research here too…)
Apparently, according to my informants, some men’s clothes shops do the same thing, but a lot don’t.
Anyway, the physics here is about reflections. Reflections off a curved surface distort the image. A convex surface (one that bulges outwards) will shorten distances whereas a concave surface (one that is indented) will lengthen them. Easy to check out with a spoon. For the clothes shop mirror, the surface must be convex in just the horizontal direction, so it makes horizontal distances appear shorter (your waistline appears thinner) but not the vertical direction, so you remain the same height. So the mirror will be approximately a section of a vertical cylinder. Turn the mirror by 90 degrees, and it will make you look shorter instead.
An extreme example of reflections comes from a perfectly reflecting sphere. In this case, the entire surrounding world gets squeezed into the image, and things appear very squashed, especially around the edges. It doesn’t matter where a light source is in relation to the viewer, the viewer will always be able to see the light source reflected in the sphere (unless it is immediately behind the sphere). A mirror ball sculpture provides a lovely example of this on campus here at Waikato, which I admit to having used as a ‘lecture’ demonstration. Have a look at this image, and see how the whole of the surroundings are reflected in it.