# Lens maker Equation Calculator

Lens maker Equation Calculator is a web-based tool that calculates the focal length of a thin lens in air given the radius of curvature. To achieve the appropriate focal distance, simply input the inputs in the tool's input area and press the calculate button.

### How do you calculate the Parameters of Lens Maker Equation?

The detailed step-by-step procedure for solving Lens maker problems is outlined below. To obtain the lens maker equation of focal length, students must carefully follow these directions.

- To calculate the focal length, enter the data’s such as the refractive index and the radius of curvature of the mediums.
- To achieve the appropriate focal distance,simply input the inputs as n, R
_{2}and R_{1} - calculate the focal length by press the calculate button.
- To get the focal length is calculated from the lens maker equation:1/f=(n - 1)*(1/R
_{1}- 1/R_{2}) - Find the relevant values in the provided formulas.
- As a result, determine the the focal length of a thin lens in air given the radius of curvature.

### The Lens Maker Formula

The focal length can be determined or estimated using the mathematical formula for lens making, which is as follows: **1/f=(n-1)*(1/R _{1} -1/R_{2})+(n-1)*d/(n*R_{1}*R_{2}))**

- Where f is the focal length and n is the lens material's refractive index.
- R
_{1}is the curvature radius of the lens surface closest to the light source - The Radius of Curvature of the Lens Surface Away from the Light Source is R
_{2}. - The thickness of the lens is denoted by the letter d

By simplifying the lens maker's formula even more by assuming the lens is very thin, i.e., d=0, we can get

1/f=(n - 1)*(1/R_{1} - 1/R_{2})

The simplified version of the formula can be used in the majority of cases since the lenses are thin enough.

**Radius of Curvature: **Radius of Curvature can be either positive or negative. Spherical lenses, in general, have two types of surfaces on the left and right sides, which might be convex or concave.

Convex Lens: left surface R_{1}>0, right surface R_{2}<0

Concave Lens: left surface R_{1}<0, right surface R_{2}>0

For more concepts check out physicscalculatorpro.com to get quick answers by using the free tools available.

### Lens Makers Equation Example

**Question 1:**If the refractive index is 2.5, the radius of curvature of Surface 1 is 4cm, and the radius of curvature of Surface 2 is 6 cm, what is the focal length of the thin lens?

**Solution:**

Consider the problem,we have,

Refractive Index, n=2.5

Curvature Radius 1, R_{1}=4cm

Curvature Radius 2, R_{2}=6 cm

Formula: We know that, the focal length of a thin lens(d=0),1/f=(n - 1)*(1/R_{1} - 1/R_{2})

By substituting the inputs in the previous formula, we get the following equation.

1/f=(2.5-1)*(1/4 - 1/6)

1/f=(1.5)*((6-4)/24)

If we simplify any more, we get

1/f=0.125

f=24 cm as the focal length.

As a result, the focal length of a thin lens for the given input is 24 cm.

### FAQs on Lens Makers Equation Calculator

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

The formula for the Lens Maker Equation: 1/f=(n-1)*(1/R_{1} -1/R_{2})+(n-1)*d/(n*R_{1}*R_{2}))] By simplifying the lens maker's formula even more by assuming the lens is very thin, i.e., d=0, we get 1/f=(n - 1)*(1/R_{1} - 1/R_{2})

**2. What are the two different types of lenses?**

Concave and convex lenses are the two types of lenses.

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

The Lens Maker's Formula's limitations are that the lens must be thin, and the medium on both sides of the lens must be the same.