# Homework Help: Range of movement of a lens?

1. Apr 25, 2012

### HenryHH

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

1/f = 1/p +1/q

3. 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...

2. Apr 25, 2012

### Staff: Mentor

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

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

3. Apr 25, 2012

### HenryHH

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

4. Apr 26, 2012

### Staff: Mentor

I wouldn't use the phrase "cancels out".  Perhaps "fades away", "disappears", or "vanishes", would be appropriate though.