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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Radius of curvature of surface #1, r1		cm
Radius of curvature of surface #2, r2		cm
Refractive index of lens material, n1		m
Refractive index of medium, n2		m

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OUTPUT   VARIABLES   &   GRAPHS

Variables	Values	Units
♦  Focal length of lens, f		cm
♦  Power of lens, P		diopters

Thin Lenses

Converging or positive spherical lens are thicker at the center than at the rim, and will converge a beam of parallel light to a real focus. Diverging or negative lens are thinner at the center and diverge light to a virtual focus.

For a lens of a known material and ground to a certain shape, it is possible to calculate the focal point in a given medium as well as its power by the lens maker’s equations:

where
     r₁ = radius of curvature of the first surface (+ve if curvature center is to the right of surface, -ve if to the left)
     r₂ = radius of curvature of the second surface (+ve if curvature center is to the right of surface, -ve if to the left)
     n₁ = refractive index of lens material, e.g. glass=1.5, ruby=1.77, iodine crystal=3.34
     n₂ = refractive index of ambient medium, e.g. vacuum=1.0, air=1.00029, water=1.333
     f = focal point (+ve if converging, -ve if diverging)
     P = lens power in diopters (m^-1)

Turning the lens around 180 deg has no effect on its focal length or power.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Bueche FJ & Hecht E; College Physics, Schaum's Outlines Series; McGraw Hill, New York, 1997.
• Lowe TL & Rounce JF; Calculations For A-Level Physics; Nelson Thornes Ltd, Cheltenham, UK, 2002