Question

In order for a film camera with a fixed focal length F to focus on anobject located a distance x from the lens, the lens must be a distance yfrom the film. F, y, and x are related as follows:

Now suppose a camera has a lens with focal length F = 65.

Explain what happens to the distance between the lens and the film as the object moves far away from the lens. When an object far away (x is near infinity), what is the internal distance from the lens and film?

Consider the opposite. Explain what happens to the distance between the lens and the film as the object moves closer and closer to the lens. Is there a distance from the lens at which you can no longer focus?

In general, why is it not possible to cross a vertical asymptote?

What is focal length, and how does it work?

Answer 1

1/F = 1/x +1/y

Rearranging the aove equation :

1/y = 1/F-1/x = (x-F)/xF

1/y =(x-F)/xF

y = xF/(x-F) ; Given F= 65

y = 65x/(x-65) = 65/( 1-65/x)

If  the object moves far away from the lens i.e. x increases 65/x decreases (1-65/x) increases, y decreases

If you decrease the x distance from the lens, then y increases.

A vertical asymptote occurs where the function is undefined so, if the line were to cross a vertical asymptote, then for some input(s) you would have more than one value that that input maps to, thus the line wouldn't be a function anymore.

A horizontal asymptote is only concerned with end behavior; there is no requirement for the function to not have the value of the y-coordinate of a point on the asymptote.