Assuming uniform probability for all points in base area A, the associated probability of an apex ray of length L through a given point in A is P(dA) = 1/A x r x dr x dw where r is the radius from the center of base to the specified point and w is the corresponding central azimuthal angle...
Consider an oblique circular cone of altitude h, base radius R, with apex directly above a point on the base circumference. What is the mean length (& variance) for the set of all rays from the apex to points on or within the base circumference?
Thanks for the reference, I'll check it out.
My own intuitive approach to this issue is as follows:
if the original empty containing volume were filled with an incompressible fluid, and then supposing that each molecule added to the volume could/would displace an equal volume of fluid out...
Thanks Phillip: orthodox explanation too neat to be true
The total excluded volume of an isolated molecule (under the hard sphere assumption) is as you say 8 times the volume of the molecule itself.
In a collision pair, the actual total excluded volume (and the bounding surface area) attending...
Consider a unit volume (rigid walled container of surface area S) containing N molecules with diameter d, having a maxwellian speed distribution with a mean time between collisions t*.
Allowing for a stable (i.e constant) equilibrium mono-layer distribution of some number of these molecules...
Hey MFB!
Thanks for your reply, but I'm not sure how to diagrammatically set-up or mathematically carry out the transformation you're talking about.
Say the mirror is moving away from the light source (along the direction of it's normal with fixed velocity v) and the light ray is incident...
Question:
Does the law of specular reflection (angle in = angle out) for obliquely incident light rays still hold if the mirror is translating in a direction parallel to its normal direction?
If not, what different effects attend said translation if
a) the motion is toward or away from...