What Is the Focusing Range for a 45 mm Lens on an SLR Camera?

AI Thread Summary
The discussion centers on determining the focusing range for a 45 mm lens on a 35 mm SLR camera, specifically for distances from infinity to 1.4 m. Using the thin-lens formula, it is established that the lens must move from 45 mm to approximately 46.49 mm to achieve this focus range. A participant seeks clarification on how to handle the concept of infinity in the lens equation, realizing that 1/∞ effectively approaches zero. The conversation highlights that 1/∞ can be interpreted as negligible, simplifying the equation. Overall, the key takeaway is understanding how to apply the thin-lens formula in practical scenarios involving varying object distances.
HenryHH
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Homework Statement



In a 35 mm single lens reflex camera (SLR) the distance from the lens to the film is varied in order to focus on objects at varying distances. Over what range must a lens of 45 mm focal length vary if the camera is to be able to focus on objects ranging in distance from infinity down to 1.4 m from the camera?

Homework Equations



1/f = 1/p +1/q

The Attempt at a Solution



First, the thin-lens formula is applied for the case of focusing on objects at a distance of infinity:

1/45 = 1/∞ + 1/q
q = 45 mm

Then, the same formula is applied for the case of focusing on objects at a distance of 1.4 mm:

1/45 = 1/1400 + 1/q
q = 46.49 mm

Therefore, the range of movement is 46.49 - 45 = 1.49 mm.

I actually had help from a tutor with solving this problem. I understand the problem itself, but what I don't understand is how q = 45 was derived from the equation 1/45 = 1/∞ + 1/q since the equation contains ∞ as a variable.

Generally speaking, how do you solve equations with infinity (∞) as one of the variables? I am really stumped...
 
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1/∞ is a very tiny number, called zero. :smile:

So 1/p = 1/q, giving p=q
 
OH... so 1/infinity basically just cancels out, then? Duh... thanks!
 
HenryHH said:
OH... so 1/infinity basically just cancels out, then? Duh... thanks!
I wouldn't use the phrase "cancels out".
mVVtk.gif
 Perhaps "fades away", "disappears", or "vanishes", would be appropriate though.
 
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