Question

You visit your eye doctor and discover that you require lenses having a diopter value of -8.4 . Are you nearsighted or farsighted? With uncorrected vision, how far away from your eyes must you hold a book to read clearly?

Short answer

Answer: A person with a diopter value of -8.4 is nearsighted. To read a book clearly without correction, they should hold it approximately 11.9 centimeters away from their eyes.

Step-by-step solution

Determine if the person is nearsighted or farsighted

A diopter is a unit of measurement for the optical power of a lens. A positive diopter value indicates farsightedness (difficulty in seeing things close-up), while a negative diopter value indicates nearsightedness (difficulty in seeing things far away). Since the given diopter value is -8.4, the person is nearsighted.

Calculate the focal length

To determine the comfortable reading distance for the person, we will use the formula for the focal length (f) of a lens: f = 1 / D where D is the diopter value. In this case, D = -8.4, so: f = 1 / (-8.4) = -0.119 meters, or -11.9 centimeters Since the focal length is negative, it indicates that the focal point is on the same side of the lens as the object being viewed. This is a characteristic of a diverging lens, which is used to correct nearsightedness.

Determine the distance to hold the book

The comfortable reading distance is determined by the focal point of the uncorrected vision. As the focal length is -11.9 centimeters, the person must hold the book at approximately 11.9 centimeters away from their eyes to read it clearly without correction.