If a man’s face is 30 cm in front of a concave shaving mirror creating an upright image \( 1.5 \) times as large as the object, then the mirror’s focal length is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( -90 \) cm
A concave mirror gives an upright, magnified image only when the object is between the pole and the focus; the image is then virtual and behind the mirror. Use the mirror formula with the Cartesian sign convention (distances measured from the pole, positive behind the mirror).
\( u = -30\,\mathrm{cm} \)
\( m = +1.5 \text{ (upright)} \)
\( m = -\frac{v}{u} \Rightarrow v = -mu = -(1.5)(-30) = +45\,\mathrm{cm} \)
\( \displaystyle \frac{1}{f} = \frac{1}{v}+\frac{1}{u} = \frac{1}{45}-\frac{1}{30} = \frac{2-3}{90} = -\frac{1}{90} \)
\( f = -90\,\mathrm{cm} \)
The negative sign confirms a concave mirror; its focal length is 90 cm.