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You buy a magnifying glass at the store. The lens in the magnifying glass is a double convex lens, a lens with two convex curved surfaces. You determine the focal length of the lens is +25 cm. Of both sides of the lens have about the same radius of curvature and the lens is made of a glass with index of refraction 1.6, what is the radius of the glass surfaces?

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Answer:

30 cm

Explanation:

f = Focal length = 25 cm

R = Radius of curvature (both sides are equal)

[tex]\mu[/tex] = Refractive index of lens = 1.6

The lens maker formula is given by

[tex]\frac{1}{f}=(\mu-1)(\frac{1}{R_1}-\frac{1}{R_2})\\\Rightarrow \frac{1}{f}=(\mu-1)(\frac{1}{R}-\frac{1}{-R})[/tex] minus sign because it is on the other side

[tex]\\\Rightarrow \frac{1}{f}=(\mu-1)\frac{2}{R}\\\Rightarrow R=2(\mu-1)f\\\Rightarrow R=2(1.6-1)\times 25\\\Rightarrow R=30\ cm[/tex]

The radius of curvature of the glass surface is 30 cm

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