. A myopic person having far point 80 cm uses spectacles of power –1.0 D. How far can he seeclearly?
Question
A myopic person having far point 80 cm uses spectacles of power –1.0 D. How far can he see clearly?
Solution
The power of a lens is given by the formula:
P = 1/f
where P is the power of the lens and f is the focal length. The power of the lens is given in diopters (D) and the focal length is given in meters.
In this case, the power of the spectacles is -1.0 D. This means that the focal length of the lens is -1.0 m (since 1 D = 1 m^-1).
The far point of a myopic person is the maximum distance at which they can see clearly. In this case, the far point is 80 cm or 0.8 m.
The lens formula is given by:
1/v - 1/u = 1/f
where v is the image distance (which is the far point for a myopic person), u is the object distance (which is infinity for a distant object), and f is the focal length of the lens.
Substituting the given values into the lens formula, we get:
1/0.8 - 1/∞ = -1
Solving for v, we get:
v = 1/ [(1/-1) + (1/∞)] = 1/ [-1 + 0] = -1 m
However, since distance cannot be negative, we take the absolute value of v, which gives us v = 1 m.
Therefore, with the spectacles, the person can see clearly up to a distance of 1 meter.
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