An object is placed 40 cm in front of a convex mirror of radius of curvature 20 cm. The image is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → virtual and 8 cm behind the mirror
The image follows from the mirror equation \( 1/v+1/u=1/f \) with the Cartesian sign convention. In this convention, distances are measured from the pole, and those behind the mirror are positive. The focus of a convex mirror lies behind it, so its focal length is positive.
\( u=-40\,\mathrm{cm} \)
\( \begin{aligned} f &= \frac{R}{2} \\ &= \frac{+20\,\mathrm{cm}}{2} \\ &= +10\,\mathrm{cm} \end{aligned} \)
\( \begin{aligned} \frac{1}{v} &= \frac{1}{f}-\frac{1}{u} \\ &= \frac{1}{10\,\mathrm{cm}}+\frac{1}{40\,\mathrm{cm}} \\ &= \frac{5}{40\,\mathrm{cm}} \end{aligned} \)
\( v=+8\,\mathrm{cm} \)
The positive sign places the image 8 cm behind the mirror. The reflected rays do not meet there. They only appear to come from that point, so the image is virtual.