Ball Lens Focal Length Calculator

How to accurately find the focal length of a ball lens? Off course you are at the best place. The following calculator provides multiple methods based on your basic to advance level knowledge that may give you an idea about ball lens focal length.

Focal length of a ball lens is the distance between the center of the ball lens. And the point where rays of light converge to give a sharp image. This feature is extremely important in several optical applications

Calculator User Guide

Step	Action
Enter Refractive Index	Input the material’s refractive index (e.g., 1.5).
Enter Ball Lens Diameter	Input the lens diameter (e.g., 10 mm).
Click Calculate	The calculator will display the focal length.

Example Input Values

Example Type	Refractive Index	Diameter	Ball Lens Focal Length
Basic	1.5	10 mm	7.5 mm
Advanced	2.0	20 mm	10 mm

Formula for Ball Lens Focal Length

 $\text{BLFL} = \frac{n \times D}{4 \times (n - 1)}$

Variable	Description
BLFL	Ball Lens Focal Length
n	Refractive Index
D	Diameter of the Ball Lens

Solved Examples

1. Basic Calculation Example

Step	Calculation
Refractive Index (n)	1.5
Diameter (D)	10 mm
Formula Input	$\text{BLFL} = \frac{1.5 \times 10}{4 \times (1.5 – 1)}$
Simplify Denominator	$\text{BLFL} = \frac{15}{4 \times 0.5}$
Calculation	$\text{BLFL} = \frac{15}{2} = 7.5$

Answer: The ball lens focal length is 7.5 mm.

2. Advanced Calculation Example

Step	Calculation
Refractive Index (n)	2.0
Diameter (D)	20 mm
Formula Input	$\text{BLFL} = \frac{2.0 \times 20}{4 \times (2.0 – 1)}$
Simplify Denominator	$\text{BLFL} = \frac{40}{4 \times 1}$
Calculation	$\text{BLFL} = \frac{40}{4} = 10$

Answer: The ball lens focal length is 10 mm.

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Ball Lens Focal Length Calculator