(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.
To determine if you are nearsighted or farsighted, we need to compare the refractive power of your eye with the standard values.
(a) The refractive power of your relaxed eye is given as 56.0 D (diopters), and the lens-to-retina distance is 2.35 cm.
A nearsighted eye has excessive refractive power and causes light to focus in front of the retina. On the other hand, a farsighted eye has insufficient refractive power and causes light to focus behind the retina.
Using this information, we can determine whether you are nearsighted or farsighted by calculating the focal length (f) of your eye using the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the eye,
- v is the image distance (distance from the retina), and
- u is the object distance (distance from the lens).
Given the lens-to-retina distance (v) as 2.35 cm, we can substitute the values into the lens formula. Since the object distance (u) for relaxed vision is considered infinity for simplicity, we can ignore the 1/u term (as 1/infinity becomes 0):
1/f = 1/v
1/f = 1/2.35 cm
Now, let's solve for the focal length (f):
f = 2.35 cm
If the focal length (f) is positive, it indicates that the light converges (in front of the retina), which means you are nearsighted. Thus, if your calculated focal length is positive, you are nearsighted.
(b) If you are nearsighted, to determine your far point, we need to find the distance at which you can see objects clearly without needing to accommodate. This point is referred to as the far point.
In this case, we can use the lens formula and the concept of far point to determine it. The far point is the distance from the lens (eye) to the object when the object is at infinity.
Using the lens formula, we have:
1/f = 1/v - 1/u
Let's assume that the far point is at infinity, so the object distance (u) becomes infinity.
Since the formula becomes:
1/f = 1/v
Substituting the calculated focal length (f) into the equation (which we found from the previous question), we can solve for v:
1/(2.35 cm) = 1/v
Solving for v:
v = 2.35 cm
Therefore, the far point for a nearsighted individual in this case is 2.35 cm from the lens or eye.
If you are farsighted, to determine your near point, follow the same process by substituting negative values for the refractive power and calculating the focal length as we did in part (a). Then the near point would be calculated using similar methods as the far point for nearsighted individuals.
(a) To determine if you are nearsighted or farsighted, we can use the formula for calculating the lens power:
Lens Power = 1 / Focal Length
Focal Length = 1 / Lens Power
Given that the lens-to-retina distance is 2.35 cm and the refractive power of your relaxed eye is 56.0 D, we can find the focal length as follows:
Focal Length = 1 / (56.0 D)
To convert from diopters (D) to meters (m), we use the conversion factor: 1 D = 1 m^-1.
Focal Length = 1 / (56.0 m^-1)
Focal Length = 0.0179 m
(b) If you are nearsighted, the far point is the farthest distance at which you can see clearly without the aid of corrective lenses. The far point for a nearsighted person is located at infinity.
If you are farsighted, the near point is the closest distance at which you can see clearly without the aid of corrective lenses. The near point for a farsighted person is located at a finite distance.
Given that you have a refractive power of 56.0 D, which indicates nearsightedness, your far point is infinity.