Finding fmax in Thin Lens Refraction Problem

[icedragon]

Homework Statement

Hi all. This is a problem from one of the problem sheets from earlier in the term. I'm just revising for my exam tomorrow and can't solve this one. Here it is:

Consider a light source placed at a fixed distance L from a screen, such that a lens of focal length
f can be placed between the source and the screen. Show that as long as f < fmax there are two
positions where the lens can be placed so that an image is formed on the screen, and find a value for fmax.

Homework Equations

1/s + 1/s' = 1/f

The Attempt at a Solution

I substituted in s' = L-s which gives me:

1/s + 1/(L-s) = 1/f

Given that there are two solutions and the nature of that formula I am guessing I need a quadratic equation and then to solve for s. Not sure how to expand that equation so I can solve for s?

Thanks

 

[darkxponent]

multiply both sides by s(L-s) and you will get a quadratic equation.

 

[barryj]

So far so good. f and L are constants, right? Merely solve for s. Yep, you might a quadratic equation with two solutions.

 

[icedragon]

Thanks for the help. Got the equation in the form (1/f)s^2 - (L/f)s + L = 0 giving the solutions s= (L±sqrt((L/f)^2 - (4L/f))/2

Does that look good? Lecturer hasn't published answers to this problem sheet for some reason. :(

 

[barryj]

your quadratic equation loo0ks good. I assume you are using the quadratic formula to solve for s. Just make sure you use the quad formula correctly. Note that when the lens is close to the object, the image is large, and when the lens is close to the screen, the image is small.

 

[icedragon]

Yep I used the quadratic formula. Thanks for your help. :)