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Video transcript

great work now that you know what's going on to make a sharp image let's calculate exactly where the point of sharp focus is we know the point where the medial and parallel rays intersect again let's put the origin of our coordinate system at the center of the lens and let the point to be focused have coordinates X 0 and y 0 the medial ray passes through the origin and the point X 0 y 0 so the line equation for it is just y equals y 0 divided by X 0 times X the parallel ray passes through two points we know the point on the lens it hits which is at 0 y 0 and the focal point of the lens which is at minus F 0 it has a slope y 0 over F and y intercept at y 0 so the equation of this line is y equals y 0 over F times X plus y 0 to intersect these lines we set these equations equal to one another we have y 0 over X 0 times x equals y 0 over f times X plus y 0 then we divide through by y 0 to give 1 over x 0 times x equals 1 over F times X plus 1 and now let's divide through by x which gives us 1 over x 0 equals 1 over F plus 1 over X notice the X in this equation is the x-coordinate where the lines intersect according to our diagram this happens when x equals minus I our diagram also tells us that X 0 is equal to the object distance oh so we have 1 over o equals 1 over F minus 1 over I which we usually rewrite as 1 over o plus 1 over I equals 1 over F tada this is called the simple lens law it says that an object at distance o from the lens with focal length F comes into focus at distance I in the next exercise we'll test your understanding of this idea