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## Homework Statement

An object is placed 6 metres from a convex lens of focal length 30cm. A concave lens of focal length 5cm is then placed 20 cm from the concave lens, on the side distant from the object.

Determine the position, magnification and nature of the final image formed (to solve the problem apply the lens-makers formula twice).

## Homework Equations

Lens makers equation. I assume of the thin lens form (1/p + 1/q = 1/f)

## The Attempt at a Solution

Applying the thin lens formula upon the initial lens, it tells me that an image is produced 31.5cm to the right (assuming working left to right) of the lens. That bit I understand.

However, the other lens is placed 20cm to the right of the first, and as a result the image produced by the first lens hasn't formed at this point. So, from what I can understand from my textbook and notes the rays then head back to being paralell.

But, I also saw that a focal length for a diverging lens is negative, so does that mean that I can say that the object is 20cm away from the lens, as the rays start to bend there? Combining this with the focal length of -5cm, and putting into the thin lens equation will give an image distance of -0.04m, or 4 cm to the left of the concave lens.

So does this mean that the image will be formed inbetween the two different lenses?

If this is the correct distance, does this mean that the magnification is 1/95th of the original size? And the image will also be inverted (I assume that this is what the question means by the nature of the image).

Is this right, or have I gone wrong somewhere?