The power (in diopters) of an equiconvex lens with radii of curvature ...
The focal length of a lens is given as
Here, n = 1.6. R
1 =0.1 m. R
2 = - 0.10 m
So,
= (0.6) (20)
1/f =12
⇒ Power P = 1/f = +12D
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The power (in diopters) of an equiconvex lens with radii of curvature ...
The power of an optical lens is a measure of its ability to bend light rays. It is represented in diopters (D) and is defined as the reciprocal of the focal length in meters. The power of a lens depends on its curvature and refractive index.
Given information:
- Radii of curvature (R) = 10 cm = 0.1 m
- Refractive index (n) = 1.6
To find the power of an equiconvex lens, we can use the lens maker's formula:
1/f = (n - 1) * (1/R1 - 1/R2)
where f is the focal length, R1 and R2 are the radii of curvature of the two lens surfaces.
Calculating the focal length:
Since the lens is equiconvex, the radii of curvature are equal, i.e., R1 = R2 = 0.1 m.
1/f = (1.6 - 1) * (1/0.1 - 1/0.1)
1/f = 0.6 * (10 - 10)
1/f = 0
From the equation, we can see that the focal length is 0, which means the lens is a plane sheet of glass and does not converge or diverge light. Therefore, the power of the lens is zero diopters.
However, if we assume that the lens is not equiconvex and has different radii of curvature for each surface, we can calculate the power using the lens maker's formula. Let's assume the lens is convex on both sides with radii of curvature R1 and R2.
Calculating the power:
1/f = (n - 1) * (1/R1 - 1/R2)
1/0 = (1.6 - 1) * (1/R1 - 1/R2)
0 = 0.6 * (1/R1 - 1/R2)
Since the lens is equiconvex, R1 = R2 = 0.1 m. Substituting these values into the equation:
0 = 0.6 * (1/0.1 - 1/0.1)
0 = 0.6 * (10 - 10)
0 = 0
Again, we find that the focal length is 0, and therefore, the power of the lens is zero diopters.
So, there seems to be an error in the given answer. The correct power for an equiconvex lens with radii of curvature of 10 cm and a refractive index of 1.6 is 0 diopters, not 12 diopters.