Final answer:
To see what he is doing when he shaves, a nearsighted man needs to stand at a distance from the mirror that is less than his near point of 20 cm.
Step-by-step explanation:
In order for the nearsighted man to see what he is doing when he shaves, he must stand closer to the mirror. The distance from his eyes to the mirror should be less than his near point of 20 cm. Let's say the distance is 'd' cm. According to the property of a concave mirror, the object distance and image distance are positive when they are on the same side as the object, which is in this case. The formula for the mirror equation is: 1/f = 1/u + 1/v, where 'f' is the focal length of the mirror, 'u' is the object distance, and 'v' is the image distance. Since the object and image are on the same side of the mirror, the image distance 'v' will be negative. The object distance 'u' will be positive, and the focal length 'f' will also be positive for a concave mirror.
Plugging in the known values, the equation becomes: 1/f = 1/u - 1/(-d). Simplifying further, we get: 1/f = (d - u)/(u * d).Since the man can see objects clearly up to 20 cm away, we can set 'u' to 20 cm. The equation now becomes: 1/f = (d - 20)/(20 * d). By solving this equation, we can find the value of 'd' which represents the distance the man needs to stand from the mirror in order to see what he is doing when he shaves.