Finding the focal length of a diverging lens in a two-lens system

[vucollegeguy]

Homework Statement

A small object is 25.0 cm from a diverging lens as shown in the figure . A converging lens with a focal length of 11.4 cm is 30.0cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens.

The Attempt at a Solution

1/f = 1/o + 1/i at every step

conv lens

1/12 = 1/o + 1/17.0

o = 40.8

This means the second object, which is the first image, was 40.8 cm to the left of the conv lens.

This means the second object was 40.8 - 30 = 10.8 cm to the left of the div lens

So the image distance for the div lens is -10.8 and

1/f = 1/25.0 + 1/(-10.8)

1/f = 0.04 - 0.0926 = -0.05259

f = -19.0 cm is the focal length of the div lens

 

[collinsmark]

Hello vucollegeguy,

Homework Statement

A small object is 25.0 cm from a diverging lens as shown in the figure . A converging lens with a focal length of 11.4 cm is 30.0cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens.

The Attempt at a Solution

1/f = 1/o + 1/i at every step

conv lens

1/12 = 1/o + 1/17.0

o = 40.8

Where do you get a length of 12 cm? The problem statement says that the converging lens has a focal length of 11.4 cm. You might want to correct this before you move on. 'Turns out it makes a significant difference in the end.

 

[vucollegeguy]

I changed 12 to 11.4. My final answer came out to be -5.6 but distance can't be negative. Is my answer correct?

 

[collinsmark]

I changed 12 to 11.4. My final answer came out to be -5.6 but distance can't be negative. Is my answer correct?

Correct me if I'm wrong, but I thought you were solving for the focal length of the diverging lens. Focal lengths of diverging lenses are negative by definition.