Question

The ratio of size of image to that of the object in a pinhole camera.

Answer 1

Answer:

The size of a pinhole camera” is ambiguous. As Martin Sol assumes, you could be talking of something like the distance from the hole to the image formed. That’s simple: any distance will do, since there is no focus.

However, you can think in terms of focal length, and I assume that’s what you are really thinking of. Let’s take the lens formula

1/u+1/v=1/f

u is the object distance, v is the image distance, and f is the “focal length”. As I said, you can choose any v, and you will get an equally good f. So by itself, this doesn’t help you much, unlike with a lens.

But then you have the magnification m. And there’s another formula:

m=v/u

So you can substitute and get:

v=um

1/u+m/u=1/f

1+m=u/f

f=u/(1+m)

And that’s what you’re looking for. Note that the object size is irrelevant.

Answer 2

Answer:

Answer:

The size of a pinhole camera” is ambiguous. As Martin Sol assumes, you could be talking of something like the distance from the hole to the image formed. That’s simple: any distance will do, since there is no focus.

However, you can think in terms of focal length, and I assume that’s what you are really thinking of. Let’s take the lens formula

1/u+1/v=1/f

u is the object distance, v is the image distance, and f is the “focal length”. As I said, you can choose any v, and you will get an equally good f. So by itself, this doesn’t help you much, unlike with a lens.

But then you have the magnification m. And there’s another formula:

m=v/u

So you can substitute and get:

v=um

1/u+m/u=1/f

1+m=u/f

f=u/(1+m)

And that’s what you’re looking for. Note that the object size is irrelevant.