Question:
A dentist uses a mirror of focal length \(24\,\text{mm}\). He views a cavity in the tooth of a patient by holding the mirror at a distance of \(16\,\text{mm}\) from the cavity. The magnification is
A dentist uses a mirror of focal length \(24\,\text{mm}\). He views a cavity in the tooth of a patient by holding the mirror at a distance of \(16\,\text{mm}\) from the cavity. The magnification is
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For a concave mirror, when the object is placed between the pole and focus, the image formed is virtual, erect and magnified. Use
\[
m=-\frac{v}{u}
\]
after applying the mirror formula.
Updated On: Jul 29, 2026
- \(2\)
- \(3\)
- \(1\)
- \(1.5\)
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The Correct Option is B
Solution and Explanation
Concept:
A dentist uses a
concave mirror to obtain a magnified virtual image of the tooth. The mirror formula is \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}. \] Magnification is \[ m=-\frac{v}{u}. \]
Step 1: Write the sign convention values. For a concave mirror, \[ f=-24\,\text{mm}, \qquad u=-16\,\text{mm}. \]
Step 2: Find the image distance using the mirror formula. \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}. \] Substituting, \[ \frac{-1}{24} = \frac{1}{v} - \frac{1}{16}. \] \[ \frac{1}{v} = -\frac{1}{24} + \frac{1}{16}. \] \[ = \frac{-2+3}{48}. \] \[ = \frac{1}{48}. \] Hence, \[ v=48\,\text{mm}. \]
Step 3: Calculate the magnification. \[ m = -\frac{v}{u}. \] \[ = -\frac{48}{-16}. \] \[ =3. \] Therefore, \[ \boxed{m=3} \] \[ \boxed{\text{Answer = (B)}} \]
concave mirror to obtain a magnified virtual image of the tooth. The mirror formula is \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}. \] Magnification is \[ m=-\frac{v}{u}. \]
Step 1: Write the sign convention values. For a concave mirror, \[ f=-24\,\text{mm}, \qquad u=-16\,\text{mm}. \]
Step 2: Find the image distance using the mirror formula. \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}. \] Substituting, \[ \frac{-1}{24} = \frac{1}{v} - \frac{1}{16}. \] \[ \frac{1}{v} = -\frac{1}{24} + \frac{1}{16}. \] \[ = \frac{-2+3}{48}. \] \[ = \frac{1}{48}. \] Hence, \[ v=48\,\text{mm}. \]
Step 3: Calculate the magnification. \[ m = -\frac{v}{u}. \] \[ = -\frac{48}{-16}. \] \[ =3. \] Therefore, \[ \boxed{m=3} \] \[ \boxed{\text{Answer = (B)}} \]
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