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A dentist uses a mirror in front of a decayed tooth at a distance of $4 cm$ from the tooth to get four times the magnified image in the mirror. What is the focal length and nature of the mirror used.?

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6.44 cm

, convex mirror

- 5.33 cm

, concave mirror

10 cm

, plane mirror

None of the above

answer is B.

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Detailed Solution

The Focal length of the mirror,

f = - 5.33 cm

, and the mirror is concave.
The image formed by the dentist's mirror is erect. Hence, as per the question, the distance of the object, and magnification,

m = + 4

We know

m = - \frac{v}{u}, hence

v = - mu

\Rightarrow - (+ 4) \times (- 4) = 16 cm

\Rightarrow \frac{1}{f} = \frac{1}{v} + \frac{1}{u}

\Rightarrow \frac{1}{16} + \frac{1}{- 4}

\Rightarrow \frac{1 - 4}{16}

\Rightarrow - \frac{3}{16}

\Rightarrow f = - \frac{16}{3}

= - 5.33 cm

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