Question

A w0cm high object is placed on the principal axis at a distance 12 cm from the pole . If the image is inverted real and 5 cm high find the focal length of the mirror and the location of the image?

Answer 1

Answer on Question #62131-Physics-Optics

A 2.5 cm high object is placed on the principal axis at a distance 12 cm from the pole. If the image is inverted real and 5 cm high find the focal length of the mirror and the location of the image?

Solution

$$\frac{1}{u} + \frac{1}{v} = \frac{1}{f}.$$ $$m = -\frac{5}{2.5} = -2.$$ $$m = -2 = -\frac{v}{u} \rightarrow v = 2u.$$ $$\frac{1}{u} + \frac{1}{2u} = \frac{1}{f}$$ $$\frac{3}{2u} = \frac{1}{f}$$

The focal length of the mirror is

$$f = \frac{2}{3}u = \frac{2}{3}(-12) = -8 \text{ cm}.$$ $$v = 2u = 2(-12) = -24 \text{ cm}.$$

The image is formed at a distance 24 cm from the pole.

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