Your friend is far-sighted with a near-point distance of 512 cm. What should the focal length be for the lenses in his reading glasses? Assume the glasses are placed 2.0 cm in front of his eyes.
To determine the necessary focal length for your friend's reading glasses, 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 (distance from the lens to the far point of clear vision)
- u is the object distance (distance from the lens to the near point of clear vision)
Given:
- The near-point distance (u) is 512 cm
- The glasses are placed 2.0 cm in front of his eyes
First, let's convert the near-point distance from centimeters to meters:
u = 512 cm = 5.12 m
Since the glasses are placed 2.0 cm in front of his eyes, the object distance (u) becomes:
u = 5.12 m + 0.02 m = 5.14 m
Next, we need to find the image distance (v). In this case, since your friend is far-sighted, the image distance is the distance from the far point of clear vision (infinity).
So, v = infinity, which can be approximately considered as v = ∞
Plugging the values into the lens formula, we get:
1/f = 1/∞ - 1/5.14 m
As 1/∞ approaches 0, we can simplify the equation to:
1/f = 0 - 1/5.14 m
1/f = -1/5.14 m
Now, we can solve for the focal length (f) by taking the reciprocal of both sides:
f = -5.14 m
Since the focal length cannot be negative, we take the magnitude of f:
f = 5.14 m
Therefore, the focal length for your friend's reading glasses should be 5.14 meters.