# Explanation of problem 2074 in Lim-Yung-Kuo's Problems and solutions in Optics

A pinhole camera consists of a box in which an image is formed on the film plane which is a distance P from a pinhole of diameter d. The object is at a distance L from the pinhole, and light of wavelength $$\lambda$$ is used (Fig. 2.66).

Approximately what diameter d of the pinhole will give the best image resolution?

The solution goes something like this :

He says because of geometric optics we see a bright ring of diameter, $$\Delta_1$$ and it is found using the relation: $$\frac{\Delta_1}{L+P} = \frac{d}{L}$$.

Then he says because of diffraction we also see a bright airy disk of diameter $$\Delta_2$$ and $$\Delta_2= \frac{\lambda P}{d}$$

He then says the sum of diameter is minimum for best resolution and gets $$d$$.

Doubt: The image will be formed because of diffraction and hence there would be an airy disk but why would image formed by geometric optics is separately considered? (I understood how the diameter due to geometric optics is calculated).

Also, why should the sum of diameters is minimum for best resolution, won't the centers of both disks would same ?(i.e point where the horizontal line intersects the screen). I don't get why the sum of diameters is minimum?

• I've added the homework-and-exercises tag. In the future, please use this tag on this type of question. – user4552 Mar 4 '19 at 15:29