The Lens Maker’s Formula - Definition, Solved Examples, FAQs

In this article, we will discuss about, what is lens maker’s formula? What is radius of curvature of lens? What is lens maker formula for concave lens? What is lens maker equation? What is relation between focal length and refractive index? What is curvature of lens? So let’s see,

What is lens maker’s formula?

Lens is a refracting object (device), which include of a transparent material. It can have 2 curved s/f (surfaces) or 1 curved and 1 plane s/f (surface). Basically, lenses can be categorized or classified as convex (converging) and concave lenses (diverging).

Definition: Real lenses have the limited thickness between their two exterior/surfaces of curvature. An ideal thin lens with two surfaces of uniform curvature will have zero refracting (optical) power. It means it wills neither convex nor concave light. A lens with some thickness which is not trivial is called a thick lens.

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The focal length of a lens depends on the index of refraction (refractive index) of the lens and the radii of curvature. The lens maker’s equation is second formula used for lenses that provide us a relationship betwixt the focal distance (length), index of refraction, and radii of curvature of the two spheres used in lenses. It is employed by lens manufacturers to form the lenses of particular power from the glass of a given index of refraction.

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Lenses are of two kinds based on the curvature of the two refracting surfaces. Convex and concave.

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What is lens maker’s Equation?

Lens maker’s Equation/formula for thin lens:

Lens maker formula is used to assemble a lens with the itemize focal length. A lens has 2 curved surfaces, but these are not exactly the selfsame. If we know the index of refraction and the radius of the curvature of both the surface, then we can find out the focal length of the lens by using the given lens maker’s formula:

1/f=(μ-1)×(1/R1 - 1/R2)


f=focal length of the lens

μ= Refractive index

R1 and R2 = Radius of the curvature of both 2 surface

It is signify that the lens should be thin so that the segregation betwixt the two refracting surfaces should be small. Also, the medium on either side of the lens should be the equal or same.

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Lens maker’s Equation/formula for thick lens:

Lenses where the thickness is minor, such that they are considered negligible in contrast to the radius of curvature, are mentioned to as thin lenses.

If the thickness of lens has to be considered in comparison to the radius of curvature, the below lens formula for thick lenses can be used.

1/f=(n-1)[1/R1 - 1/R2 + (n-1)d/(n×R1 R2) ]


d = thickness of the lens in consideration

While, another concept that has to be contemplated is the lens maker’s formula accounting for objects that are present in divergent media. The equation is as given,


n1 = refractive index of the lens in consideration

n2 = refractive index of the external medium

Related Topics Link,

  • Determination Of Focal Length Of Concave Mirror And Convex Lens
  • Power of a Lens Ray Optics
  • Spherical Mirror Formula
  • Mirror Formula for Spherical Mirrors
  • Uses of Convex Lens

What is lens maker formula for convex lens?

If the ambient medium is taken to be air i.e. n1≈1 and n2= n is taken into account, the optician formula are often given within the usual form.

Lens Maker Formula for Concave Lens and Convex Lens

For a concave lens, R1 is -ve and R2 is +ve. The lens maker formula for concave lens is represented as,

1/f=-(n2/n1-1)[1/R1 + 1/R2]

For a convex lens, R1 is +ve and R2 is -ve. The lens maker formula shown in the form,

1/f=(n2/n1-1)[1/R1 + 1/R2]

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