Physics · Reflection of light, spherical mirrors, mirror formula
A beam of light converges towards a point behind a convex mirror of focal length
A beam of light converges towards a point \( 0, \) behind a convex mirror of focal length \( 20 \mathrm{cm} . \) Find the magnification and nature of the image when point 0 is \( 30 \mathrm{cm} \) behind the mirror.
- A. 2 (virtual, inverted)
- B. 3 (real, inverted)
- C. 3, (virtual, enlarged)
- D. +1 (real, enlarged)
Step-by-step solution
Using the mirror formula 1/v + 1/u = 1/f with sign convention: convex mirror f = +20 cm. Since the object O is behind the mirror (virtual object), u = +30 cm. Then 1/v = 1/20 - 1/30 = 1/60, so v = +60 cm. Positive v indicates image behind mirror (virtual). Magnification m = -v/u = -60/30 = -2. Negative m means inverted image. Hence magnification is 2 (absolute value) and image is virtual, inverted.
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