A person has a far point of 20 cm. What power glasses would correct this vision if the glasses were placed 1.9 cm from the eye?
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To determine the power of the glasses needed to correct a person's vision, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens (in meters)
- v is the image distance from the lens (in meters)
- u is the object distance from the lens (in meters)
In this case, the person's far point is given as 20 cm, so we need to find the focal length that corresponds to this distance.
Given:
- Far point (v) = 20 cm = 0.20 m
- Distance of the glasses from the eye (u) = 1.9 cm = 0.019 m
Rearranging the equation, we get:
1/f = 1/v - 1/u
Substituting the given values:
1/f = 1/0.20 - 1/0.019
Simplifying further:
1/f = 5 - 52.63
Now, let's calculate:
1/f = -47.6
To find the power of the lens, we can use the formula:
Power (P) = 1/f
Substituting the value of 1/f:
P = 1/(-47.6)
Calculating further:
P = -0.021 D
Therefore, the power of the glasses needed to correct this person's vision would be approximately -0.021 D. It is important to note that the negative sign indicates that the lens should be concave (diverging) to correct the far point vision.