Lenses and mirrors

Chen

It's a known fact that when you partially cover a lens (with fabric or something), the image on the other side would look less illuminated, since less light rays go through the lens.

However, what happens when you partially cover a concave/convex mirror? Our teacher thinks the same thing happens, the image looks less illuminated. I, and some other pupils, think that by covering the mirror you reduce the "field of eyesight", i.e the number of places from which you can fully see the object in the mirror.

Can anyone confirm either claims, and explain why? [:)]

Loren Booda

We agree that for both mirror images, less light is apparent in general. Depending on the resolution of the observer, say on the scale of the rods and cones in his eye corresponding to the effective diffraction of the cloth and to (well-ground) mirror magnification, constructive or destructive interference can take place.

The interference depends upon the wavelength of light, the size of the cloth aperture, distance and angle to the observer, and whether or not he is involved classically. One analogy (not immediately obvious) might be two polarizers oriented either perpendicular or parallel to each other, with an intermediate fine cloth grid of arbitrary orientation.

That the mirror is well ground helps determine the coherence of interference. If the cloth is less than a few wavelengths from the mirror, the interference effect may be greatly distorted.

Njorl

When you say you are covering part of the mirror with cloth, do you mean you put cloth on a fraction of the mirror, or you cover the whole mirror, but the loose weave of the cloth lets some light through?

Njorl

Chen

I mean covering part (like half) of the lens/mirror with cloth that won't let light get through. I noticed I had misled Loren Booda, I'm sorry.

Loren Booda

's OK. An interesting thought experiment, anyway.

Doc Al

An interesting question, Chen!

Here's my take: I think it depends on whether the mirror produces a real image or a virtual image. For a real image, all parts of the mirror carry light that contributes to the image. For a virtual image, only the piece of mirror that you are actually looking at reflects the light that hits your eye.

Check out an ordinary plane mirror. The image is virtual and clearly isn't affected by blocking off half the mirror. Also check out a magnifying glass, which also produces a virtual image (in normal use). Blocking off half the lens doesn't matter. But if I use the magnify glass to form a real image (like of the sun when you wish to start a fire), covering up half the lens will degrade the image (and the amount of light that is focused). (I used these examples since that's what I have handy.)

Of course if you block off so much of the lens/mirror that diffraction effects dominate, all bets are off. :-)

Chen

Thanks Doc Al, I was thinking along the same line. I'll speak with my teacher and let you know what she says (I'm fairly certain we are right though).