- #1

JulienB

- 408

- 12

## Homework Statement

Hi everybody! Being given three identical thin lenses with the same focal length, I have to determine ##a## (distance object-screen), ##d_a## (distance lens 1-lens2) and ##d_b## (distance lens 2-lens 3) so that a sharp image of the object appears on the screen regardless of the position of the optical system between the object and the screen (see picture).

## Homework Equations

Lens equation: ##\frac{1}{f} = \frac{1}{s_i} + \frac{1}{s_o}## with ##s_i##: distance from lens to screen and ##s_0##: distance from lens to object.

## The Attempt at a Solution

Well I didn't get very far because I don't really know what is the condition for an image on the screen to be sharp. Is it the case

*only*when the lens equation is fulfilled, that is when I have a certain ##s_i## and ##s_o## so that the sum of their inverses is equal to ##1/f##?

And if so, is the following thinking correct? Say a ray of light is going from ##S## to ##L_1##. I want it to be sharp when meeting ##L_2##, so the following equation has to hold:

##\frac{1}{x} + \frac{1}{d_a} = \frac{1}{f}##.

Is that correct? If so I can set up an equality with three equations, but I am afraid it remains dependent of ##x## then. Any clue about how to tackle such problems?Thanks a lot in advance for your answers.