This can be used only when the lens is kept in air. Where n is absolute refractive index and this equation is called lens maker's formula.

NOTE:

Always use sign convention while using any formula derived in this chapter and the above formula can be used for any thin lens. The convex lens behaves as a converging lens, if it is kept in a medium with refractive index less than the refractive index of the lens. It behaves like a diverging lens when it is kept in a transparent medium with greater refractive index than that of the lens. For example an air bubble in water behaves like a diverging lens. Let us see an example for lens maker formula

Example 7

What is the focal length of double concave lens kept in air with two spherical surfaces of radii R₁= 30cm and R₂=60cm. Take refractive index of lens as n = 1.5.

Solution:

From the figure E-7 using sign convention we get R₁= -30cm, R₂ = 60cm and also given that n = 1.5

using 1/f = (n-1)(1/R₁ – 1/R₂)

1/f = (1.5 - 1)[1/(-30)-1/60]

Solving this, we get

f = -40cm

Here minus indicates that the lens is divergent

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