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# An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

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An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

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Given: u = -10 cm, f = 15 cm and v = ?

Applying the formula $$\frac{1}{f}$$ = $$\frac{1}{v}$$ + $$\frac{1}{u}$$, we get

$$\frac{1}{15}$$ = $$\frac{1}{v}$$ - $$\frac{1}{10}$$

⇒ $$\frac{1}{v}$$ = $$\frac{1}{15}$$ + $$\frac{1}{10}$$

= $$\frac{2+3}{30}$$ = $$\frac{5}{30}$$ = $$\frac{1}{6}$$

⇒ v = 6 cm

Hence, the image is formed behind the mirror. It is erect, virtual and smaller than the object.

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