Range of movement of a lens?

[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.

 

[asteriatic]

The concept of infinity (∞) can be difficult to grasp, but in mathematics, it is often treated as a limit or a value that is larger than any real or imaginable number. In the context of this problem, the distance from the lens to an object at infinity is essentially the same as the focal length of the lens, since the object is so far away that the light rays can be considered parallel. Therefore, we can substitute ∞ for the distance in the thin-lens formula, and solve for q. This gives us q = 45 mm, which means that the lens must be positioned at a distance of 45 mm from the film in order to focus on objects at infinity.

To solve equations with infinity as a variable, we can apply the same principles as we would with any other variable. In this case, we can manipulate the equation algebraically to isolate the variable (q in this case) and solve for it. In some cases, we may also need to use limits or other mathematical techniques to find a solution. It is important to keep in mind that infinity is not a number, but rather a concept that we use in mathematics to represent something that is unbounded or without limit.