At what two distances could you place an object from a 45-cm-focal-length concav

Question

At what two distances could you place an object from a 45-cm-focal-length concave mirror in order to get an image 1.5 times the objects size?

Explanation / Answer

Given, focal length,f = -45cm Magnification , m = 1.5 m = |v/u| => v = ±1.5u applying mirror formula, 1/f = 1/v + 1/u => -1/45 = ±1/(1.5u) + 1/u taking + sign => -1/45 = 1/1.5u + 1/u => -1/45 = 5/3u => 3u = -45*5 => u = -75 cm now taking - ve sign => -1/45 = -1/1.5u + 1/u => -1/45 = 1/3u => 3u = -45 => u = -15 cm Hence if we place object at 15 cm or 75 cm from concave mirror thenwe will get image 1.5 times greater than object

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