The right lens of Josh's contact lenses is a converging lens of +2.50 diopters. He can read a book held as close as 25 cm from his eyes.

Question

The right lens of Josh's contact lenses is a converging lens of +2.50 diopters. He can read a book held as close as 25 cm from his eyes. Complete the following statement: Without his lenses, Josh's right eye has

A) a far point of 15.4 cm.

B)a far point of 40.0 cm.

C) a far point of 66.7 cm.

D) a near point of 15.4 cm.

E) a near point of 66.7 cm.

Please show the work and explain.

Answer 1

A converging lens is a corrective measure for hyperopia, meaning that a person is "farsighted" or can see sharply from "infinity" up to a "near point" but must have corrective lenses to see acutely from the near point up to his eyes.

The Lens Equation gives 1/p + 1/q = 1/f where p is the object distance, q (in this case) is the negative of the image distance and f is the focal length equal to one over the power given in diopters. From the given information, one can rewrite the Lens Equation as

1/p + 1/(-0.25) = 1/(1/2.5) which simplifies to 1/p − 4 = 2.5 or 1/p = 6.5 or p = 0.153846153846153846... meters equivalent to 15.4 centimeters.

Josh then has (D) a near point 15.4 centimeters from his right eye.