Josh Pendreigh, of Mosgiel West School, asks :-
Why is it that when I look into my dinner spoon my reflection is smaller than me?
John Campbell, who teaches optics at the University of Canterbury, responded.
Let us make a few more observations. Take two identical, shiny, spoons, preferable soup spoons because they have nearly spherical curvature. Place them side-by-side but one back uppermost and the other front uppermost. The image from the latter is upsidedown but notice that the two images are of the same size.
For a regular dinner spoon or teaspoon, which has different curvatures across the spoon compared with along the spoon, note that the image of your head is longer than it is wide. Rotate the spoon and you will see the image become wider than it is long.
Now lay in a row back uppermost, a tea spoon, a soup spoon, a dinner spoon and a flat mirror. Choose this series so that they are in order of the amount of curvature. Note that the image size is larger the flatter (ie the least curved) the spoon is. For the flat mirror (any flat shiny surface will do) the image is full size.
All of these observations show that the image size depends on the amount of curvature of the reflecting surface. The tighter the curvature, the smaller the image appears to be. Spherical mirrored Christmas tree ornaments are very good for these observations. Using ray optics we can work out the size of the image for any given curvature and position of the object being looked at.
Now take your biggest, least curved spoon. Hold it at arms length, with the bowl towards you. Bring it towards your eye. Note that the image is upside down and gets larger and larger until it becomes the right way up. Ray optics tells us this switch-over occurs when our eye is half the distance between the mirror and its centre of curvature.
A shaving or make-up mirror would be even better for these observations. These have a large radius of curvature (they are flatter than spoons). In normal use we place our face closer than half the radius of curvature distance in order to get a magnified image the correct way up. (The magnified image is also handy for locating sqeezeable blackheads.) Now move your head away from the mirror. Note that the image of your head gets bigger until it flips upside-down then gets smaller as you continue moving away. Now you have the same situation as looking into a spoon.
You may be able to find a piece of shiny plastic sheet which is flexible. I cut a piece from a soft drink bottle. This allows you to alter the radius of curvature and to see the image change in size and also to invert as you switch from having it curving outwards to curving inwards.