# A converging lens is made with glass with refractive index 2.1. If the radius of the two curved surfaces is the same and equal to 4 cm, what is the focal length of the lens.

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### 1 Answer

The focal length of a lens, converging or diverging, can be determined from the lens maker's formula: `1/(f) = (n - 1)(1/R_1 - 1/R_2 + ((n-1)*d)/(n*R_1*R_2))` where `R_1` is the radius of the curved surface closer to the object, `R_2` is the radius of the other curved surface, n is the refractive index of the material that the lens is made of and d is the thickness of the lens.

In the problem, the thickness of the lens is not given. A simplified version of the formula applicable to thin lenses can be applied `1/f = (n-1)(1/R_1 - 1/R_2)` . The radius of both the curved surfaces is 4 cm and the refractive index of the glass is 2.1. This gives the focal length of the lens as: `1/f = (2.1 - 1)(1/4 + 1/4)` = `1.1*1/2` = 0.55

=> f = 1/0.55 = 1.81 cm

The focal length of the lens is approximately 1.81 cm