How Do You Calculate Focal Length in a Two-Lens System?

[jones123]

Homework Statement

An object is placed at 25 cm to the left of a diverging lens. A converging lens with a focal length of 12 cm is located 30 cm to the right of the diverging lens. The two-lenses-system forms a real inverted image 17 cm to the right of the converging lens (see attachment).

Homework Equations

What is the focal length of the diverging lens?

The Attempt at a Solution

I know that
1/f = 1/v - 1/b
For the converging lens I got:
1/12 = 1/v - 1/(-17) => v = 40.8 cm
For the diverging lens I got:
1/f = 1/40.8 - 1/(-30) => f = 17.29 cm

The correct answer should be -19 cm.

Thanks for the help!

 

[ehild]

Homework Statement

An object is placed at 25 cm to the left of a diverging lens. A converging lens with a focal length of 12 cm is located 30 cm to the right of the diverging lens. The two-lenses-system forms a real inverted image 17 cm to the right of the converging lens (see attachment).

Homework Equations

What is the focal length of the diverging lens?

The Attempt at a Solution

I know that
1/f = 1/v - 1/b
For the converging lens I got:
1/12 = 1/v - 1/(-17) => v = 40.8 cm
For the diverging lens I got:
1/f = 1/40.8 - 1/(-30) => f = 17.29 cm

The correct answer should be -19 cm.

Hi Jones123, welcome to PF.
The equation for the diverging lens is not correct. The object distance is 25 cm, and the image distance is also wrong. 40.8 cm is the distance from the converging lens, which is 30 cm to the right of the diverging one.

ehild

 

[barryj]

"For the diverging lens I got:
1/f = 1/40.8 - 1/(-30) => f = 17.29 cm" this is incorrect.
What is the object distance?
What is the image distance?