Question

the distance between the pinhole and the screen in a pinhole camera is doubled from 20cm to 40cm. how will it affect the image of an object kept a distance of 20 cm in front of the pinhole?

Answer 1

Magnification= Li/Lo = Di/Do.

Let us 1st take the case when distance is not doubled:.

In this case Lo =Lo and Li = Li and Di = 20cm and Do =20cm.

We get Li = Lo that is the length of the object and the length of image is equal.

In this case Lo =Lo and Li = Li and Di = 40cm and Do = 20cm.

We get Li = 2Lo that is the length of the image becomes twice the image of the object.

Answer 2

At double the distance from the pinhole to the screen one quarter the amount of light will fall on the screen (much darker) the area of the image of the object which remains the same distance in front of the pinhole will be 4 times larger on the screen and the edges twice as fuzzy (on each side).

Pinhole Camera Design Calculator is a link to a calculator I have used on occasion. According to that page for optimal results the 20 cm pinhole/screen case should have a pinhole 0.596 mm in diameter (f/336) but at 40 cm the size of the pinhole can be increased to 0.853 mm (f/471).

If you do that my first paragraph does not apply.