A patient has a far point of 34.6 cm and a near point of 26.0 cm. What power (in diopters) should be prescribed to give the patient normal vision for:
(a) contact lenses?
1) D
(b) glasses which are worn 0.9 cm away from the patient's eyes?
2) D
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To determine the power (in diopters) of contact lenses or glasses that should be prescribed for a patient, we can use the formula:
Power (P) = 1 / focal length (f)
where the focal length is the reciprocal of the distance in meters.
(a) For contact lenses:
The patient's far point is 34.6 cm, so the focal length for contact lenses would be 1 / 0.346 = 2.89 meters.
Therefore, the power of the contact lenses should be 1 / 2.89 = 0.346 D.
(b) For glasses worn 0.9 cm away from the patient's eyes:
Since the glasses are worn 0.9 cm away from the eyes, we need to consider the equivalent focal length, taking into account the additional distance.
The equivalent focal length (fe) can be calculated by summing the individual distances involved:
1 / fe = 1 / f1 + 1 / f2
Where f1 is the distance between the glasses and the patient's eyes and f2 is the focal length of the eyes.
Given that the glasses are worn 0.9 cm away (0.009 meters), and the near point is 26.0 cm (0.26 meters), we can calculate fe:
1 / fe = 1 / 0.009 + 1 / 0.26 = 287 / 2.34
fe = 2.34 / 287 = 0.0081 meters
Therefore, the power of the glasses should be 1 / fe = 1 / 0.0081 = 123.46 D.
In summary,
(a) The power of the contact lenses should be 0.346 D.
(b) The power of the glasses worn 0.9 cm away from the patient's eyes should be 123.46 D.