The lens maker’s equation is a formula that gives us a relationship between the focal length, refractive index, and radii of curvature of the two spheres used in lenses.
- Use:
- To manufacture lenses of the desired focal length.
- Dependency:
- Refractive index of the lens and the radii of curvature.
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The Lens Maker’s Equation for Thin Lenses:
Lenses where the thickness is lesser, such that they are considered negligible in comparison to the radius of curvature, are referred to as thin lenses.
where,
f is the focal length (half the radius of curvature)
n is the refractive index of the material used
R1 is the radius of curvature of sphere 1
R2 is the radius of curvature of sphere 2
As previously mentioned, this equation can be used only for thin lenses. Lenses where the thickness is lesser, such that they are considered negligible in comparison to the radius of curvature, are referred to as thin lenses.
If the thickness of the lens has to be considered compared to the radius of curvature, the following lens formula for thick lenses can be used.
where,
d is the thickness of the lens in consideration.
Another situation that has to be considered is the lens maker’s formula accounting for objects that are present in different media. The equation is as follows,
where,
n1 is the refractive index of the lens in consideration
n2 is the refractive index of the medium outside
Have you asked yourself this question? “What is the significance of ignoring the thickness sometimes and considering it sometimes?”
Well, the answer to that is when the light ray travels from a medium of, say air to the medium of the lens, it undergoes refraction. But when it travels from the medium of the lens to that of the air, it undergoes refraction again. The double refraction can be ignored if the lenses in optics are thin enough to make the assumption that light is refracted only once. This is done to simplify ray optics calculations, but the first step would be identifying what constitutes thin and thick lenses.
Limitations of Lens Maker’s Formula
- The lens needs to be thin. This is because separating the two refracting surfaces will also be small.
- The medium on either side of the lens needs to be the same.
In violation of the limitations, the refraction at the curved surface formula is used for both surfaces.
Helpful Sign Conventions
- For a Convex (converging) Lens
R1 = positive
R2 = negative
f = positive
- For a Concave (diverging) Lens
R1 = negative
R2 = positive
f = negative
If the focal length is positive, then the lens is said to be converging, and if the focal length is negative, then it is said to be diverging. From this, we can come to the conclusion that a convex lens doesn’t necessarily have to be converging and concave diverging.
Stay tuned with “BYJU’S – The Learning App” to learn about the concave and convex lens and much more.
Frequently Asked Questions – FAQs
What is a lens?
A lens is a piece of transparent material or glass with curved sides for dispersing or focusing light rays.
What are the two common types of lenses?
The two most common types of lenses are convex and concave lenses.
What is a contact lens?
A contact lens is a specially designed thin lens placed directly above the viewing plane of the eyes. They are worn to correct vision problems or for therapeutic and cosmetic reasons.
What is the use of the lens maker’s formula?
Lens manufacturers use the lens maker’s formula to manufacture lenses of the desired focal length. Lenses of different focal lengths are used for different optical instruments.
What is the connection between the focal length and the refractive index of a lens?
The focal length of a lens depends on the refractive index of the lens and the radii of curvature.
What is Lens Maker’s Formula?
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