Physics

Physics

Problem

A concave mirror has a focal length of 10 cm10\,\text{cm}. A candle is placed 15 cm15\,\text{cm} in front of the mirror on the principal axis. Without calculating the exact image distance, determine whether the image is (i) real or virtual, (ii) upright or inverted, and (iii) enlarged, reduced, or the same size as the candle.
Intuitive explanation

The key is recognizing that the object distance and focal length determine the image type through one simple rule: when the object sits between the focal point and center of curvature (f<do<2ff < d_o < 2f), light rays converge after reflection to form a real, inverted image on the same side as the object. Since 15 cm15\,\text{cm} falls exactly in this zone (between 10 cm10\,\text{cm} and 20 cm20\,\text{cm}), you can predict all three properties without the mirror equation—real images from concave mirrors are always inverted, and this particular position produces magnification greater than 1.

Intuitive explanation

The key is recognizing that the object distance and focal length determine the image type through one simple rule: when the object sits between the focal point and center of curvature (f<do<2ff < d_o < 2f), light rays converge after reflection to form a real, inverted image on the same side as the object. Since 15 cm15\,\text{cm} falls exactly in this zone (between 10 cm10\,\text{cm} and 20 cm20\,\text{cm}), you can predict all three properties without the mirror equation—real images from concave mirrors are always inverted, and this particular position produces magnification greater than 1.

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