Finding lens diameter - German physics task

[Matt_]

Thank you, due to your explanation I've understand it better.

Are you familiar with Geometric Optics?

I think yes, I understand the ray diagram (and how a image is transmitted). But somehow I don't get the relation between the lamps and the diameter.

https://en.wikipedia.org/wiki/Circle_of_confusion

Ohh, sorry for my stupidity:

The circle of confusion in the image plane is obtained by multiplying by magnification m: (Wikipedia)

c = diameter of the blur spot * magnification (1)

Is this right?

 

[Lok]

I think yes, I understand the ray diagram (and how a image is transmitted). But somehow I don't get the relation between the lamps and the diameter.

Hi Matt_,
The relation you search for is between the spot diameter and the focused image of the ruler. That is to say that for this special case (thin lens and all idealizations), for any lens focal length the result is the same.
Also this would be the reason why a smartphone with it's 2mm (at best) diameter will NEVER take a picture like this one https://en.wikipedia.org/wiki/Bokeh#/media/File:Josefina_with_Bokeh.jpg with the blurred background. It simply cannot do it unless the subject is very small (~10mm) an close to the camera lens (under ~20mm), conditions which cannot be met with the focus of a normal smartphone.

 

[Matt_]

Hi Matt_,
The relation you search for is between the spot diameter and the focused image of the ruler. That is to say that for this special case (thin lens and all idealizations), for any lens focal length the result is the same.
Also this would be the reason why a smartphone with it's 2mm (at best) diameter will NEVER take a picture like this one https://en.wikipedia.org/wiki/Bokeh#/media/File:Josefina_with_Bokeh.jpg with the blurred background. It simply cannot do it unless the subject is very small (~10mm) an close to the camera lens (under ~20mm), conditions which cannot be met with the focus of a normal smartphone.

Thanks to all, I understand the problem now :)

 

[Merlin3189]

Sorry to question the consensus about a diagram being the solution, (though I always sketch a diagram or two to help me visualise the situation and mark on my symbols.)

I thought of one position for the ruler and screen, where you would not even need a diagram to work out the lens diameter (u = v = 2f, M =1, spot size = D)
Then I thought, there are many other positions where the ruler and screen could be, so I resorted to calculation to show that the special case gives the same result as the general one. But, how can you get this general result from a geometric diagram? Would you not have to draw an infinite number of diagrams? I had to use an inaccurate symbolic diagram and algebra (though pretty simple algebra.)

 

[mfb]

The focal points don't matter. There are four rays to consider: two parallel ones from the distant light source, and two parallel ones from two points on the ruler, where the previous two rays go through. We don't know any distances, but we know the two light rays in the pairs ("up", "down") will hit the same spot each (because they have identical trajectories). All other rays from the ruler will hit the same spot as well as the ruler is in the focus.
One diagram catches all possible cases.

 

[Merlin3189]

Thanks. Took me a while to follow you without a diagram, but once I draw it I see what you mean. You guys obviously have more imagination than me.