# Optical Instruments two lenses

## Homework Statement

A 2 cm tall object is 20 cm to the left of a lens with a focal length of 10 cm. A second lens with a focal length of 15 cm is 30 cm to the right of the first lens. Calculate the image position and height. Compare with ray-tracing.

## Homework Equations

1/f = 1/do + 1/di, m = -di/do and hi/ho; f: focal point, do: object distance, di: image distance, hi: image height, ho: object height.

## The Attempt at a Solution

1/dia = 1/10 - 1/20, dia=20 cm; 1/dib = 1/15 - 1/(-dia+30), dib=-30 cm. (a denotes first lens, b second).
And this is where I stumble. Looking in the back of the book, the correct answer seems to be: dib=30 cm, hib=6.0 cm. Doing the previous problems, the measurements are relative from the second lens, and after comparing the result with my ray diagram 30 cm, or -30 cm for that matter, is no where near my second image convergence point.

You seem to be right. The second lens form the image at -30cm with a magnification of x3. So the image formed by the 2nd lens will be inverted and 6cm high.

Have you tried making a ray diagram?

No, these are just from the thin lens formula. Do you have a problem with constructing the diagram?

I must be, because when I construct the diagram, the location of the second image is neither 30 cm in front of or behind the second lens, which doesn't lend our answer much levity.

ray diagram

The image op the tip of the arrow, p, will seem to be located at p' if you extend the rays backwards.
That is if one looks to the left through the lens the rays seem to originate from the point p'.

#### Attachments

• ray diagram.pdf
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