An object is placed in front of a convex mirror of focal length 10" " cm, at a distance of 15" " cm. Its image is formed at a distance of and is

Correct option is D

Given:

​$$f$$= focal length = 10 cm (Positive for convex mirror)

$$u$$ = -15cm (Negative, as the object in front of the mirror.)

Formula used:

Mirror formula: $$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$ 

Solution:

Substitute values: $$\frac{1}{10} = \frac{1}{-15} + \frac{1}{v}$$ 

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

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

$$\frac{1}{v} = \frac{3}{30} + \frac{2}{30}$$ 

$$\frac{1}{v} = \frac{5}{30}$$ 

Take reciprocal to find $$v$$ :$$v = \frac{30}{5} = 6 \, \text{cm}$$ 

$$v = 6 \, \text{cm}$$ , image is virtual, upright, and diminished behind the mirror.

Thus the correct answer is (D)

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