Nechama Z.

asked • 05/13/20# 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.

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.

## 1 Expert Answer

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.**

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Stanton D.

Hi Nechama Z., without even an equation you can eliminate all choices but (E). Why? Since he needs a converging lens, his own eye isn't convergent enough. That means, he can't focus on near objects. Without the contact, the near limit of his convergence must therefore be further away than 25 cm. Search up an equation for combining lenses and apply it. -- Cheers, -- Mr. d.05/19/20