(a) If your relaxed eye has a refractive power of 56.0 D, and your lens-to-retina distance is 2.35 cm, determine if you are nearsighted or farsighted.
(b) If you are nearsighted, determine your far point. If you are farsighted, determine your near point.
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To determine if you are nearsighted or farsighted, you need to compare the refractive power of your eye with the lens-to-retina distance.
(a) If your eye's refractive power is greater than the lens-to-retina distance, then you are nearsighted. If it is smaller, then you are farsighted.
In this case, your relaxed eye has a refractive power of 56.0 D and a lens-to-retina distance of 2.35 cm. To compare these values, we need to convert the lens-to-retina distance from centimeters to meters, since the refractive power is given in diopters (D).
Lens-to-retina distance = 2.35 cm = 0.0235 m
Now, let's compare the refractive power and the lens-to-retina distance:
Refractive power (in D) = 56.0 D
Lens-to-retina distance (in m) = 0.0235 m
Since the refractive power is greater than the lens-to-retina distance, you are nearsighted.
(b) If you are nearsighted, your far point is the distance at which the light coming from a far object is focused in front of your retina, resulting in a blurred image. To determine the far point, you can use the formula:
Far point = 1 / (Refractive power)
Where the refractive power is given in diopters. In this case, the refractive power is 56.0 D:
Far point = 1 / (56.0 D)
Calculating the value:
Far point = 1 / (56.0 D) = 0.0179 meters or 17.9 cm
So, if you are nearsighted, your far point is approximately 17.9 cm.
If you are farsighted, your near point is the distance at which clear vision becomes difficult for nearby objects. To determine the near point, you can use the same formula:
Near point = 1 / (Refractive power)
Using the refractive power value of 56.0 D:
Near point = 1 / (56.0 D)
Calculating the value:
Near point = 1 / (56.0 D) = 0.0179 meters or 17.9 cm
Hence, if you are farsighted, your near point is also approximately 17.9 cm.