Question

(a) Use conceptual arguments to show that the intensity of light (energy per unit area per unit time) reaching the film in a camera is proportional to the square of the reciprocal of the f-number, as follows:

I ∝1/(f/D)^2

(b) The correct exposure time for a camera set to f/1.8 is (1/500) s. Calculate the correct exposure time if the f-number is changed to f/2 under the same lighting conditions. (Note: "f/2," on a camera, means "an f-number of 2.")

Answer 1

(a) the definition of the intensity is given as ameasure of the rate at which energy is received by the film per unit area of the image or it is alsoexpressed as I proportional to (1 / Aimage)

the intensity of the light reaching the film isalso proportional to the area of the lens to the square of the diameter of the lens I proportional to (D^2) I proportional to (D2 /f2)

I proportional to (f-number)2 ==> I ∝ (f)^2

Therefore, I ∝1/(f/D)^2

(b) Let 't' be the exposure time, then as the total light energy hitting the film isproportional to the product of the intensity and exposure time (I t)

so in oeder to maintain correct exposure, thisproduct must be kept constant.

so we get

I2 * t2 = I1 * t1