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

[HenryHH]

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...

 

[NascentOxygen]

1/∞ is a very tiny number, called zero.

So 1/p = 1/q, giving p=q

 

[HenryHH]

OH... so 1/infinity basically just cancels out, then? Duh... thanks!

 

[NascentOxygen]

OH... so 1/infinity basically just cancels out, then? Duh... thanks!

I wouldn't use the phrase "cancels out".

 Perhaps "fades away", "disappears", or "vanishes", would be appropriate though.