Question

a concave mirror forms the real image of an object which is magnified four times .the object is moved 3cm away .the magnification of the image is 3 times what is focal length?

Answer 1

Answer on Question #62130-Physics-Optics

A concave mirror forms the real image of an object which is magnified four times. The object is moved 3cm away - the magnification of the image is 3 times. What is focal length?

Solution

$$m = -4 = -\frac{v}{u}.$$ $$m' = -3 = -\frac{v'}{u - 3}$$ $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{v'} + \frac{1}{u'}$$ $$\frac{1}{4u} + \frac{1}{u} = \frac{1}{3u'} + \frac{1}{u'}$$ $$\frac{1}{4u} + \frac{1}{u} = \frac{1}{3(u - 3)} + \frac{1}{u - 3}$$ $$u = -45 \text{ cm}$$ $$v = 4(-45) = -180 \text{ cm}$$ $$\frac{1}{f} = \frac{1}{-45} + \frac{1}{-180}$$ $$f = -36 \text{ cm}.$$

Answer: $-36 \text{ cm}$.

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