A person can see an object in focus only if the object is no farther than 35 cm from the right eye and 58 cm from the left eye. Write a prescription for the refractive powers ℛ (in diopters) for the person's corrective lenses.

right eye dpt
left eye dpt

To determine the refractive powers (ℛ) for the person's corrective lenses, we need to calculate the lens power needed to bring the far point of each eye to infinity.

The far point (F) of an eye is the maximum distance at which a person with normal vision can see an object clearly without accommodation (focusing effort). In this case, the person can see an object in focus if it is no farther than 35 cm from the right eye and 58 cm from the left eye.

To convert the distance in centimeters to diopters, we use the formula:

ℛ (dpt) = 1 / F (m)

Where:
ℛ = Refractive power of the lens (in diopters)
F = Far point distance (in meters)

For the right eye:
F = 35 cm = 0.35 m
ℛ (right eye) = 1 / 0.35 = 2.86 dpt

For the left eye:
F = 58 cm = 0.58 m
ℛ (left eye) = 1 / 0.58 = 1.72 dpt

Therefore, the prescription for the person's corrective lenses is:
Right eye: +2.86 diopters
Left eye: +1.72 diopters