Final answer:
The closest distance at which the person can stand from the mirror to clearly see the reflection of the vase is 24 cm, which is option C, as this is the closest standard distance not less than their near point of 25 cm when you subtract the distance to the object in the mirror (8 cm).
Step-by-step explanation:
In this physics problem, we are trying to find the closest distance d a person with a near point of 25 cm can stand from a mirror to clearly see the reflection of a vase that is 8 cm in front of it. To determine this, we must remember that the distance to the image in the mirror is equal to the actual distance to the mirror plus the distance from the mirror to the object. Hence, the image of the vase forms 8 cm behind the mirror, appearing as if it were 16 cm from the person (8 cm to the mirror plus 8 cm behind the mirror).
Since the person's near point is 25 cm, they should stand at a point where the distance to the image is not more than 25 cm. This means the person can stand up to (25 cm − 8 cm) = 17 cm away from the mirror itself. Given the options, the closest standard distance without going below 17 cm is 24 cm (Option C), as the person would not be able to focus at 16 cm because it is less than their near point.