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Answer :
Using the lensmaker's equation with an index of refraction of 1.55, the focal length |f| of the lens is found to be approximately 4.94 meters, and the power |P| is approximately 0.20 diopters.
To determine the magnitude of the focal length |f| and the power |P| of a lens using a plastic material with an index of refraction of 1.55, the lensmaker's equation is utilized.
Given that the radius of curvature for one side of the lens is 1.10 m (which we will call R1), and for the other side is 1.85 m (R2), the equation takes the following form:
1/f = (n - 1) * (1/R1 - 1/R2)
Substituting the given values into the equation, we get:
1/f = (1.55 - 1) * (1/1.10 - 1/1.85)
1/f = 0.55 * (1/1.10 - 1/1.85)
= 0.55 * (0.909 - 0.541)
= 0.55 * 0.368
1/f = 0.2024
Therefore, the focal length |f| is:
f = 1 / 0.2024
≈ 4.94 m
To compute the lens power |P|, which is measured in diopters (D), we use the formula P = 1/f (where f is in meters).
So:
|P| = 1 / 4.94
≈ 0.20 D
This gives us the magnitude of the lens power.
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