00:01
So this question gives us two light sources that are six meters apart.
00:05
So we're going to assume that one is here and the other is here.
00:07
And we're going to say that distance between them is six meters.
00:11
And then it tells us that somewhere there is an, it says that the intensity of illumination at any point from a light source.
00:19
So wherever the illumination is, it says that the illumination, the total illumination, proportional to the square of the reciprocal distance between the point and the light source.
00:34
Okay.
00:36
So if we imagine that the illumination is equal to some constant, one over and then one over r squared, it's the square of the distance between, we're going to call it r, we call it d, i suppose.
00:51
But the total then illumination, it tells us of these two light sources, one's a stronger one.
00:59
So let's say this is the stronger one and this is the weaker one.
01:02
The total illumination is going to be k over one over x let's say if the if the illumination is somewhere in here and then plus eight times one over six minus x squared okay that's the illumination and we don't really need that constant although because it's just it's just going to stay out there but we're going to take the derivative then so we have um i'm going to leave the k out front but the derivative one over x squared is minus one over x cubed and then plus eight over minus eight over six minus x all cubed times the derivative of six minus x is minus one so i take the derivative of that and this is actually i'm actually i'm actually i'm talking about illumination actually sorry i'm talking about total illumination so i use a t sorry getting t's and i's mixed up but hopefully you can follow what i did.
02:13
So i took the illumination of both light sources, assuming that the illumination is somewhere in between them.
02:19
Okay...