The so-called \"lensmakers equation\" is shown below. The focal length of the le

Question

The so-called "lensmakers equation" is shown below. The focal length of the lens (in cm) is f. The constant n is the index of refraction of the glass, relative to the medium around it (which is just the listed value of n unless the lens is submerged in water, or some other liquid). R1 and R2 are the radii of curvature of the two sides of the lens. The value of R for a side is considered to be positive if that side is convex; otherwise, it is negative. If the lens is flat on one side, the value of R for that side is infinite, and the ratio (1/R) is equal to zero.

1/f=(n-1)(1/R_1 + 1/R_2 )

Assume the lens is biconvex; that is, that both sides are convex. The radii of curvature are both 20 cm. The coefficient of refraction is 1.40. What is the focal length of the lens, in cm?

Explanation / Answer

1/f = (1.4-1) (-1/20-1/20) 1/f = -0.4/40 f = -100 cm

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