Using the same rules for rays passing through the focal points one can derive similar results for a diverging lens. A parallel ray from the tip of the object will appear to diverge from the focal point on the left. A ray headed towards the the focal point on the right will end up traveling parallel to the optical axis. Again there are two pair of similar triangles which are associated with the focal points. Assuming o and h are initially known we get two equations for the unknowns i and y from the proportions for the triangles.
Solving for y and equating the two expressions gives another thin lens formula which is the same as the one for the converging lens if we negate the values for i and f. Again multiplying the thin lens formula by i give an expression for i/f which can be used to simplify the formula for y.
Although the position of the image has changed the magnification is again m = i/o which tells up that a line drawn through the tips of both the object and the image will pass through the center of the lens.
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