Final answer:
To find the distance from the student's eyes to the blackboard based on the eye's lens power of 51.0 D, you invert the diopter value to get the focal length. The calculated distance is approximately 19.6 millimeters, which is atypical for reading a blackboard and may indicate the use of corrective lenses or an error in the power value provided.
Step-by-step explanation:
To determine how far the blackboard is from the student's eyes, we need to understand the relationship between lens power and focal length, which is given by the formula Power (D) = 1/focal length (m).
In this case, the student's eyes have a power of 51.0 diopters (D). To find the focal length, which is the distance from the eyes to the point where the image is in focus, we can rearrange the formula to focal length = 1/power.
Therefore, the focal length (and distance to the blackboard) is 1 / 51.0 D, which equates to approximately 0.0196 meters or 19.6 millimeters.
This indicates that the student's eyes are focusing at a very close distance, typically feasible for near vision tasks, not for viewing a blackboard. This suggests that the student may be wearing corrective lenses or there is a mistake with the initial power value given for a task such as reading a blackboard.