# Lensmakers Equation Calculator

**Created By :**
Sunil Kumar Gandipadala

**Reviewed By :**
Rajashekhar Valipishetty

**Last Updated :**
May 19, 2023

Lensmakers Equation Calculator is an online tool that evaluates the focal length of a thin lens in air on providing the radius of curvature. All you have to do is enter the inputs in the input section of the tool and tap on the calculate button to obtain the desired focal length.

### Lensmakers Equation for Thin Lenses | Lensmakers Formula

You can calculate or estimate the focal length using the mathematical formula for Lens Making and it is as follows

1/f = (n - 1) * (1/R1 - 1/R2 + (n - 1) * d / (n * R1 * R2)

- Where f is the focal length
- n is the refractive index of lens material
- R1 is the Radius of Curvature of Lens Surface close to the Light Source
- R2 is the Radius of Curvature of Lens Surface farther from the Light Source
- d is the thickness of lens

Reducing the lensmakers formula further simple by assuming the lens to be very thin i.e. d = 0 we get the equation as 1/f = (n - 1) * (1/R1 - 1/R2)

In majority of the cases lenses are thin enough and we can use the simplified version of the formula.

### Radii of Curvature

Radius of Curvature can be both positive or negative. In general, spherical lenses consists of two types of surfaces on the left and right and they can be convex or concave.

- Convex Lens: left surface R1 > 0, right surface R2 < 0
- Concave Lens: left surface R1 < 0, right surface R2 > 0

**Example:** Calculate the focal length of the lens if the refractive index is 1.5, Radius of Curvature of Surface 1 is 4 cm, Radius of Curvature of Surface 2 is 6 cm?

**Solution:**

Given that

Refractive Index = 1.5

Radius of Curvature 1 = 4 cm

Radius of Curvature 2 = 6 cm

We know the focal length of a thin lens is given by 1/f = (n - 1) * (1/R1 - 1/R2)

Substituting the inputs in the above formula we have the equation as follows

1/f = (1.5-1)*(1/4-1/6)

Simplifying further we get the focal length f = 24 cm

Therefore, the focal length of thin lens for given parameters is 24 cm.

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### FAQs on Lensmakers Equation Calculator

**1. What is the Lens Maker Formula?**

Lens Maker Equation is given by the expression 1/f = (n - 1) * (1/R1 - 1/R2 + (n - 1) * d / (n * R1 * R2)

**2. What are the 2 Types of Lens?**

The 2 Types of Lenses are Concave and Convex Lenses.

**3. What are the Limitations of Lens Maker's Formula?**

The Limitations of Lens Maker's Formula is that the lens needs to be thin, medium of either sides of the lens needs to be the same.

**4. Why is it called Lens Maker Formula?**

It is a relation between the focal length of a lens to the refractive index of its material and radii of curvature of two surfaces. Since it is used by lens manufacturers in making lenses of certain power it is called as lens makers formula.