WHAT IS THE F-NUMBER OF A LENS THAT TRANSMITS TWICE AS MUCH LIGHT AS A F-4.5 LENS?
Jennifer – I apologize for this one before hand, but this is going to take some math… The amount of light transmitted by a camera lens is determined by the area of the lens s apperature. Assuming that the lens is a circle (which is not quite true, but a fair approximation), the area of the apperature equals pi times the radius squared, or A=pi*r^2. Turning this equation around gives us r=(A/pi)^1/2. The F-number of a lens is also determined by an equation. The F-number is equal to the focal length of the camera divided by the diameter of its apperature, or F=l/d. Since the diameter is equal to twice the radius, we can write this as F=l/2r. Now if we keep the focal length constant, we can put these two equations together to solve for the F-number in terms of the area of the apperature (the amount of light transmitted): F=1/2r r=(A/pi)^1/2 F=1/[2(A/pi)^(1/2)] So now we just need to plug in your numbers. If F=4.5, then we can solve the equation to give us A=0.0388. But we want the F-num
