A pinhole camera is the simplest camera possible: a closed box with a small aper

Question

A pinhole camera is the simplest camera possible: a closed box with a small aperture (a pinhole). No lens is required! A sharp inverted (upside down) image is produced (see diagram below). A bigger image is produced when you move the camera closer to the object. The pinhole should be small; a blurred image is produced by large pinholes. The optimal pinhole diameter d=v (lambda D) where lambda is wavelength of visible light and D is the focal length (distance of the screen from the pinhole). The image of an 8-m tall tree in your pinhole camera is 7 cm tall. You are standing 30 m from the tree. What is the focal length D? What should be the optimal pinhole size if you want a sharp image? (lambda for visible light is in the range 400-700 nm.)

Explanation / Answer

tree height, h=8m

image height, h'=7cm

object distance, u=30m

use,

m=-v/u=h'/h

-v/30=(7*10^-2)/(8)

===> v=-0.2625 m

image distance, v=-26.25 cm

a)

now,

1/u+1/v=1/f

1/30 + 1/(-0.2625)=1/f

====> f=-0.265 m

focal length, f=-0.265 m

b)

pin hole size, d=sqrt(lambda*f)

d=sqrt(700*10^-9*0.265)

d=0.43*10^-3 m or d=0.43 mm

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