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An object is 2 m from a lens which forms an erect image one-fourth (exactly) the size of the object. Determine the focal length of the lens. What type of lens is this?

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An object is 2 m from a lens which forms an erect image one-fourth (exactly) the size of the object. Determine the focal length of the lens. What type of lens is this?

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u = -2 m

m = +\(\frac{1}{4}\) (Erect image)

m = \(\frac{v}{u}\)

\(\frac{1}{4}\) = \(\frac{v}{-2}\)

v = -0.5 m

\(\frac{1}{v}\) - \(\frac{1}{u}\) = \(\frac{1}{f}\)

\(\frac{1}{-0.5}\) - \(\frac{1}{-2}\) = \(\frac{1}{f}\)

f = -0.666 m = -66.6 cm

It is a concave lens.

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