converging angles

Question

A 2.8 cm-tall object stands in front of a converging lens. It is desired that a virtual image 2.1 times larger than the object be formed by the lens. How far from the lens (in cm) must the object be placed to accomplish this task, if the final image is located 16 cm from the lens?

Answer 1

The only way to get a right-side-up virtual image with one lens is to have a convex lens and have the object inside the focal length. This task is only possible with a lens of a unique focal length. For the right lens you know that |m| = |d_i/d_o| = |h_i/h_o|

d_o = d_i(h₀/h_i) = 16 cm/2.1 = 7.62 cm (The only lens that this will actually work with has a focal length of

f = d_od_i/(d₀+d_i) = 14.5 cm. (Note that object is within focal length and virtual image is at -16 cm.

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