Chapter 38, Problem 38.68AP

A pinhole camera has a small circular aperture of diameter D. Light from distant objects passes through the aperture into an otherwise dark box, falling on a screen located a distance L away. If D is too large, the display on the screen will be fuzzy because a bright point in the field of view will send light onto a circle of diameter slightly larger than D. On the other hand, if D is too small, diffraction will blur the display on the screen. The screen shows a reasonably sharp image if the diameter of the central disk of the diffraction pattern, specified by Equation 37.6, is equal to D at the screen. (a) Show that for monochromatic light with plane wave fronts and L >> D, the condition for a sharp view is fulfilled if D² = 2.44λL. (b) Find the optimum pinhole diameter for 500-nm light projected onto a screen 15.0 cm away.