Question

You are to design a thin lens for eyeglasses that will have a focal length of 10 cm. You only have tools that will allow you to shape glass surfaces with the following radii for convex surfaces: 4, 8, 12, 16, 18, and 21 cm, and the following radii for concave surfaces 3, 6, 7, 10, 12 and 14 cm. The glass to be used has an index of refraction of 1.48. Determine a combination you can use to make this lens. State the radii of curvature used for each surface, and whether it is concave or convex.

Answer 1

The Lens maker's formula:

where,

• n is the refractive index of the lens material,
• f is the focal length of the lens,
• R₁ is the radius of curvature (with sign, see below) of the lens surface closer to the light source,
• R₂ is the radius of curvature of the lens surface farther from the light source.

Now sign convention for R is,

Assuming light coming from the Left to right direction,

if the center of radius is on the left of the lens the sign of R is negative
If the center of radius is on the right of the lens the sign is positive.

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From the given values of R1 and R2, here's a small python script to try out all the combinations between them and show the matches for which f = 10cm

cvex = [4, 8, 12, 16, 18, 21] cncv = [3, 6, 7, 10, 12, 14] for i in cvex:    for j in cncv:        if i == j:            continue        else:             f = (0.48*((1/-j) - (1/-i)))**-1            if f == 10 or f==-10:                print(i, j)

if you don't understand this, it doesn't matter. You can still plug in various values in the place of R1 and R2 from the given values, where R1 is the concave surface and R2 is the convex surface, and find out for which f =10, but as that'll be a bit long and tedious, so I've chosen this python script.
The Output is: 8 3
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So from the given values, when the convex surface is 8cm and the concave surface is 3cm, then focal length = 10cm.