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The far point of a myopic person is 150cm in front of the eye. Calculate the focal length and power of the lens required to enable him to see distant objects clearly

User Chargaff
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Final answer:

The myopic person requires a diverging lens with a focal length of -150cm, which translates to a lens power of -0.67 diopters, in order to see distant objects clearly.

Step-by-step explanation:

The question involves calculating the focal length and power of the corrective lens for a myopic person whose far point is 150cm. Myopia is a common vision condition, also known as nearsightedness, where distant objects appear blurry. The far point of a myopic person is the maximum distance at which they can see objects clearly.

To correct myopia, a diverging (concave) lens is required. The formula to find the focal length (f) is given by 1/f = 1/v - 1/u, where 'v' is the image distance and 'u' is the object distance. For a myopic person, the far point - which is the furthest point they can see clearly without correction - provides 'v'. Since 'v' is 150cm, the value is negative in the lens formula because the image is formed on the same side as the object. Hence, substituting 'v' = -150cm and 'u' = -∞ (for distant objects), we get 1/f = 1/(-150cm) - 1/(-∞), which simplifies to f = -150cm or -1.5m.

The power (P) of a lens is the inverse of the focal length (in meters), so P = 1/f. Thus, the power of the corrective lens would be P = 1/-1.5m = -0.67 diopters. Here, the negative sign indicates a diverging lens.

User Dave Kirby
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