Use the thin lens equation to prove that an object at infinity produces an image at the focal length of the lens (i.e. that when p = infinity, q = f). Note that q = 12.5 cm.
Added by Charles D.
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The thin lens equation is given by: \(\frac{1}{f} = \frac{1}{p} + \frac{1}{q}\) Show more…
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(a) Use the thin - lens equation to derive an expression for q in terms of f and p. (b) Prove that for a real object and a diverging lens, the image must always be virtual. Hint: Set $f=-|f|$ and show that $q$ must be less than zero under the given conditions. (c) For a real object and converging lens, what inequality involving p and f must hold if the image is to be real?
1. Prove for a converging lens, if q = p than q = p = 2f2. An object is placed 45cm from a concave lens with a focal length of 30cm. Use the thin-lens equation to determine the image distance q, the magnification factor M, and the characteristics of the image (real or virtual; upright or inverted, magnified or reduced).
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