Where can a man place his face to get an enlarged image when using a concave mirror to shave?

Analyze the question: A shaving mirror must show the face as an enlarged, upright, virtual image, so the face needs to be in a position where the concave mirror produces that kind of image.

Concept: image formation by a concave mirror

| Object position | Image | |---|---| | Beyond C | Real, inverted, diminished | | At C | Real, inverted, same size | | Between C and F | Real, inverted, enlarged (but in front of the mirror) | | At F | Image at infinity | | Between F and pole (P) | Virtual, upright, enlarged (behind the mirror) |

Solution:

• Between C and F (option A), the image is enlarged but it is real and inverted, so the man would see his face upside down. That is useless for shaving.
• At F (option B), no image forms because the reflected rays are parallel.
• At C (option D), the image is the same size as the object and inverted.
• Between F and P (option C), the image is virtual, upright and magnified. Using the mirror formula 1/f = 1/u + 1/v, when u < f, v comes out negative, which means a virtual image behind the mirror. The magnification m = |v/u| is greater than 1.

So the face must be held closer to the mirror than the principal focus.

Correct answer: C. Between the principal focus and the pole

Exam tip: Remember "inside the focus, magnify and upright". This is the same principle as a magnifying glass (a convex lens used with the object inside the focal length). Dentists' mirrors and make-up mirrors work this way too. If a question says "enlarged and upright", think "object between F and P" for a concave mirror.