20120301

Physics quiz question: myopia contact lens prescription

Physics 205B Quiz 2, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.25

A Physics 205B student with myopia has an uncorrected far point of 5.0 m. The refractive power of the contact lens used to correct this student's vision is:
(A) –∞.
(B) –5.0 D.
(C) –0.40 D.
(D) –0.20 D.

Correct answer (highlight to unhide): (D)

The uncorrected far point for this Physics 205B student is 5.0 m. This is the farthest distance do2 = +5.0 m (positive object distances correspond to being in front of the eye) that this student's unaided eye (the second lens in the two-lens contacts-eye system) can focus on, instead of the nominal far distance of ∞.

The contact lens (the first lens in the two-lens contacts-eye system) will take an object located (in front of it) at do1 = +∞, and produce a virtual image (in front of it!) at di1 = –5.0 m.

This virtual image 1 becomes the object 2 for the eye (the second lens in the two-lens contacts-eye system), which is able to see it at a distance of do2 = +5.0 m in front of it.

Solving for the focal length f1 of the contact lens:

(1/do1) + (1/di1) = (1/f1),

1/(+∞) + 1/(–5.0 m) = 1/f1,

f1 = -5.0 m.

Since contact lenses are prescribed in diopters rather than focal lengths, the refractive power (in diopters) is the inverse of the focal length (in meters):

P = (1/f1) = 1/(–5.0 m) = –0.20 D.

where the units of diopters (D) is equal to inverse meters (m–1).

(Response (C) is the inverse of the nominal near point, or 1/(+0.25 m).)

Section 30882
Exam code: quiz02gL4s
(A) : 2 students
(B) : 2 students
(C) : 5 students
(D) : 15 students

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.73

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