Question regarding a two-lens system

[pisquared]

Homework Statement

Two converging lenses, each of focal length 15 cm, are placed 20 cm apart, and an object is placed 30 cm in front of the first. Where is the final image formed and what is the magnification of the system?

Homework Equations

M_tot = M₁ * M₂
(1/f) = 1/do + 1/di

The Attempt at a Solution

[/B]
Okay, I was able to find the image distance would be 30 cm, but I have no idea how that would happen if the lenses are 20 cm apart. When drawing the ray diagram, the rays touch the second lens before converging, so I don't know where to go from there. Any help would be appreciated. Thanks!

 

[haruspex]

Homework Statement

Two converging lenses, each of focal length 15 cm, are placed 20 cm apart, and an object is placed 30 cm in front of the first. Where is the final image formed and what is the magnification of the system?

Homework Equations

M_tot = M₁ * M₂
(1/f) = 1/do + 1/di

The Attempt at a Solution

[/B]
Okay, I was able to find the image distance would be 30 cm, but I have no idea how that would happen if the lenses are 20 cm apart. When drawing the ray diagram, the rays touch the second lens before converging, so I don't know where to go from there. Any help would be appreciated. Thanks!

One way is to take the image that would be formed by the first lens and treat it as the source object for the second lens. You just have to be careful about which side the final image will be.

 

[ehild]

Okay, I was able to find the image distance would be 30 cm, but I have no idea how that would happen if the lenses are 20 cm apart. When drawing the ray diagram, the rays touch the second lens before converging, so I don't know where to go from there.

You can take that image as object of the second lens. As it is behind the second lens, take the object distance negative.

 

[pisquared]

@ehild @haruspex So the first image would go straight through the second lens and be 10 cm behind it, then be the object of the second lens?

 

[haruspex]

@ehild @haruspex So the first image would go straight through the second lens and be 10 cm behind it, then be the object of the second lens?

Yes.