# Optics problem

1. Sep 16, 2004

### kdkdkd

imagine that i have a pair of LEDs throwing light on the same point on a piece of paper. This is possible if the LEDs are inclined equally at an angle to the normal coming out of paper, right?

now if i consider two rays hitting the paper at the same point, then where can i explain the presence of the reflected ray as, is it:

1) along the normal coming out of the paper
2) partly along this normal and partly through one of the paths of incidence(since angle of incidence = angle of reflection).
3) scattered everywhere.

or is it any other answer.
help is appreciated.

2. Sep 16, 2004

### pervect

Staff Emeritus
You can start off by dividing the problem into two sections - first you figure out the contribution of one LED to what you see, then you figure out the contribution of the other LED, then you add them together. This is possible because the two LED's won't produce any interference effects, they are not coherent.

Now, when light hits a paper, some of it will reflect like a mirror, where the angle of incidence is equal to the angle of reflection. This is called specular reflection.

Other light will scatter in all directions - this is called diffuse relflection.

You'll usually see a more mathematical treatment of these sorts of problems in "ray tracing" for generation of computer images.

With flat objects, specular reflection just means glare when the object is tilted correctly, with round or curved objects (like an apple), specular reflection will create "highlights"

I didn't find anything helpful for "typical" values for specular vs diffuse reflection coefficients for paper in a quick google.

3. Sep 17, 2004

### kdkdkd

thanks a lot for your reply. it was heartening to note that there are no interference effects.... though im not entirely convinced about this. if the LEDs are of the same make, let out light in the same wavelength range, isnt the spectral equation governed by:

reflected ray property = integral ( spectral property of incident * spectral property of surface of incidence)

since both LEDs strike the same surface, the incidence surface property is also constant. so aren't they coherent??

could you enlighten me about the prominence of one particular kind of reflection over the other. If specular reflection were prominent enough, then could i successfully place a light detector between the LEDs, i.e along the normal?
thanks again.

4. Sep 19, 2004

### Claude Bile

Coherence relates to the phase of the emitted light. Photons emitted by an LED are not in phase, thus any phase dependant effects (such as interference fringes) will be washed out. Laser Diodes by contrast emit photons that are in phase, and thus will exhibit interference effects.

Claude.

5. Sep 21, 2004

### kdkdkd

thanks claude, i guess pervect was also trying to convey your idea.
my actual doubt still remains....
is it possible to place a detector between the two inclined LEDs (remember the LEDs direct light to a single point on paper) and detect the reflected light to a large extent?

good day.

6. Sep 21, 2004

### Claude Bile

Yes, if you place a detector there you will certainly detect something, how much depends on the output of the LED's, the optical noise coming from the surrounding environment, and how much the paper scatters the light.

Claude.