Question

The cemented achromate of a figure has f = 100mm. the crown glass has n1 = 1.573 and an Abbe number v1 = 57.4 and the flint glass has n2 = 1.689 and v2 = 31.2. the crown lens is symmetrical biconvex a. calculate the focal lengths f1 and f2 of the two lens. b. Calculate the radii of curvature r1, r3 (using the lens maker#s formula for thin lenses). c. Can one correct the spherical aberration by lens bending? why?

Answer 1

a.) For minimized chromatism, . And we know

Solving we get, and

Hence, f₁ = 45.6mm and f₂ = -83.97mm.

b.) Since the crown lens is symmetrical biconvex, R₁ = -R₂ (R₁ is the radius of curvature of surface 1 and is positive, R₂ And we can assume R is the radius of curvature of surface 2 or the interface between the two lenses) R₂ = R₃.

Lens maker's formula, . So, R₁ = 52.3mm. R₂ = -52.3mm

So, R₃ = -52.3mm. R₄ = -545.3mm.

c.) Yes. The focal point of a lens depends on the shape of the lens. There would be an optimal shape for the lens in which it is most close to the ideal focal length with minimal spherical aberration. Thus single lens can be bent to reduce the spherical aberration.