# Why are colours unchanged in reflections in windows?

1. Aug 22, 2014

### flutterbybrain

Not a homework question exactly, but I've been reading Feynman's QED and there's something I don't understand…

When discussing partial reflection by two surfaces, Feyman says that different thicknesses of glass reflect differed % of the incident light, transmitting the rest, and that this % also varies depending on the wavelength of light. He therefore says that if light made up of a mixture of different wavelengths is shined on a sheet of glass, the colour of the reflected light will vary with the thickness of glass because different % of the different wavelengths are reflected at each thickness. However, when sunlight reflects off windows the reflection we see is the same colour as the original image that is reflected. So, for example, the reflection of a tree in a window will still have green leaves. But shouldn't different wavelengths of light reflect more and less than each other, so the colours should be distorted?

There's definitely something I'm not getting here, any help would really be appreciated! Thanks!

2. Aug 22, 2014

### BvU

Hello Fbrain, and welcome to PF.

My Feynman QED (1961, 6th printing 1980) doesn't have an index. Whereabouts can I find this discussion ?

3. Aug 22, 2014

### Nathanael

I don't have the answer, just another question.

Why does this imply that color is distorted?

It seems to me that this effect could possibly imply that different colors of light are reflected with different intensities
(so that none of the colors are "distorted," but some colors are "easier" to see)

I don't really know how light behaves, so I'm just wondering if this is a possibility?

4. Aug 22, 2014

### haruspex

Since it discusses a relation to thickness, it has to be to do with interference between the internal and external reflections. This will vary according to the glass thickness and the wavelength.
The external reflection from glass is relatively weak, so don't expect a very strong effect. Look up Fresnel equations.

Trying to observe the effect may be complicated by polarisation. Light from a blue sky is polarised according to the direction of the light in relation to the direct light from the sun. Reflection from the glass depends on the relationship between the polarisation and the plane of reflection. This won't affect colour directly, but light from different objects may happen to be of different colour and have different polarisations, leading to the impression that some colours are reflected more strongly than others.

5. Aug 22, 2014

### ehild

The reflectance of a normal glass sheet, as windows made of, is about 4% in the visible range, and changes very little with the wavelength. It is not observable by the eye, so the colours of a mirror image are not distorted.
At the same time, if the thickness of a glass layer is comparable to the wavelength, up to a few micrometers, interference occurs between the direct reflected rays and the rays reflected from the back of the layer, and both the reflectance and transmittance changes with the wavelength and depends on the thickness. But this interference effect does not appear when the glass is more than half mm thick.

ehild

Last edited: Aug 22, 2014
6. Aug 22, 2014

### haruspex

That's 4% at each surface, yes?
Why is it limited to such thin panes? Won't there be interference when the thickness is N+1/4 wavelengths? Is it because of variations of index within the glass, or unevenness in thickness?

7. Aug 23, 2014

### ehild

Yes, 4% is the reflectance from one surface. That of a "thick" sheet is somewhat less than twice of that.
If the thickness is large, the path difference usually exceeds the coherence length. Two waves interfere if the phase difference is constant between them. The light rays come in wave "packets" and the packets have different phase constants.
The other thing is the unevenness of a glass sheet. Its thickness can be different by half-wavelength in the area where the light beam reaches it, so one part of the wave encounters constructive interference, the other does a destructive one.

Even in case you had a very good laser with long coherence length and completely parallel and smooth faces of the glass sheet, the reflectance would be a periodic function of the reciprocal wavelength. You would get minima of reflectance when 2ND=kλ and maxima if 2ND=(k+1/2)λ.
In case the refractive index of glass is N=1.5, the thickness is 1 mm, you get a minimum at λmin=400.00 nm and a maximum at 399.97 nm. You can not distinguish between wavelengths so close. It might be done with a very good spectrophotometer only.
So the transmittance and reflectance of a normal, 1-2 mm glass sheet is the average of the transmittance / reflectance you would calculate. See picture: The transmittance spectrum of a 1 mm thick microscope slide. The transmittance is nearly constant in the visible range, 400-800 nm where the absorption is very weak. The reflectance would be R=100-T (%) here. In the UV, the glass absorbs so the transmittance decreases and the reflectance also changes.

ehild

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