Lens maker\'s formula gives the focal length of a double convex lens (i.e., a le

Question

Lens maker's formula

gives the focal length of a double convex lens (i.e., a lens for which both surfaces are convex) in terms of the radii of curvature of the two surfaces. For a double concave lens (see figure below), the lens maker's formula has a slightly different form:

This relation always gives a negative focal length f as expected for a double concave lens (because it is a diverging lens). Consider such a lens composed of quartz with R1 = R2 = 45 cm and n = 1.58 for blue light. What is its focal length for blue light?
cm

Explanation / Answer

1/f-1/ (n-1)*(1/R1-1/R2)

1/f=(1/(0.58))*(4.444)=7.6628

f=0.130 m

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