A patient has a far point of 29.2 cm and a near point of 24.2 cm. What power (in diopters) should be prescribed to correct the patient's vision using:
(b) glasses which are worn 0.5 cm away from the patient's eyes?
To calculate the power of the glasses needed to correct the patient's vision, we can use the lens formula:
1/f = 1/di + 1/do
Where:
- f is the focal length of the lens
- di is the distance of the image from the lens
- do is the distance of the object from the lens.
In this case, the near point is considered the object distance (do), and the far point is the image distance (di). The patient's near point is 24.2 cm, and their far point is 29.2 cm.
First, calculate the focal length (f) using the equation:
1/f = 1/di + 1/do
1/f = 1/29.2 + 1/24.2
1/f = 0.0342 + 0.0413
1/f = 0.0755
f = 1/0.0755
f ≈ 13.25 cm
Next, we need to calculate the power of the lens, which is given by the formula:
Power (in diopters) = 1 / focal length (in meters)
Since the glasses are worn 0.5 cm away from the patient's eyes, we need to consider the effective focal length, taking this distance into account.
Effective focal length (fe) = f - d
fe = 13.25 cm - 0.5 cm
fe = 12.75 cm
Now we can calculate the power of the glasses:
Power (in diopters) = 1 / focal length (in meters)
Power = 1 / (fe/100)
Power = 1 / (12.75/100)
Power ≈ 7.84 diopters
Therefore, to correct the patient's vision using glasses that are worn 0.5 cm away from the eyes, a power of approximately 7.84 diopters should be prescribed.
To determine the power (in diopters) needed to correct the patient's vision using glasses worn 0.5 cm away from the eyes, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance (in meters)
- u is the object distance (in meters)
In this case, the object distance (u) is the distance from the glasses to the patient's eyes, which is 0.5 cm or 0.005 meters. The image distance (v) is the far point of the patient, which is 29.2 cm or 0.292 meters.
Let's plug in these values into the lens formula to calculate the focal length (f):
1/f = 1/0.292 - 1/0.005
Simplifying the equation:
1/f = (1 - 58.4)/0.005
1/f = -57.4/0.005
Now, we can calculate the reciprocal of f to determine the power of the lens (in diopters):
Power (P) = 1/f
P = 0.005/-57.4
P ≈ -0.087 diopters
So, the power prescription needed to correct the patient's vision using glasses worn 0.5 cm away from the eyes is approximately -0.087 diopters (a minus sign indicates nearsightedness).