Focusing Lens Calculator

Object Distance (p):

Refractive Index (n):

Radius 1 (r₁):

Radius 2 (r₂):

Diameter (d):

Focal Length (f):

Image Distance (q):

Magnification (m):

(unitless)

F-number (f/#):

(unitless)

1. What is a Focusing Lens Calculator?

Definition: This calculator determines the focal length, image distance, magnification, and F-number of a lens based on object distance, refractive index, radii of curvature, and diameter.

Purpose: Useful in designing optical systems like cameras, telescopes, and microscopes.

2. How Does the Calculator Work?

The calculator uses the following equations:

Step 1: Lens Maker's Equation

\( \frac{1}{f} = (n-1)\left(\frac{1}{r_1} - \frac{1}{r_2}\right) \)

Where:

\( f \): Focal length
\( n \): Refractive index
\( r_1, r_2 \): Radii of curvature

Step 2: Lens Equation

\( \frac{1}{f} = \frac{1}{p} + \frac{1}{q} \)

Where:

\( p \): Object distance
\( q \): Image distance

Step 3: Magnification

\( m = -\frac{q}{p} \)

Where:

\( m \): Magnification

Step 4: F-number

\( f/\# = \frac{f}{d} \)

Where:

\( d \): Diameter of the lens

Steps:

Enter object distance, refractive index, radii of curvature, and diameter with selected units (default cm).
Convert all inputs to centimeters for calculation.
Convert results back to the selected units and display with 2 decimal places.

3. Importance of Focusing Lenses

Focusing lenses are essential for:

Optics: Used in cameras and projectors.
Scientific Instruments: Employed in microscopes and telescopes.
Lighting: Focus light in laser systems.

4. Using the Calculator

Example 1: \( p = 20 \, \text{cm}, n = 1.5, r_1 = 10 \, \text{cm}, r_2 = -10 \, \text{cm}, d = 5 \, \text{cm} \):

Focal Length: \( \frac{1}{f} = (1.5-1)\left(\frac{1}{10} - \frac{1}{-10}\right) \), \( \frac{1}{f} = 0.5 \times 0.2 = 0.1 \), \( f = 10 \, \text{cm} \)
Image Distance: \( \frac{1}{10} = \frac{1}{20} + \frac{1}{q} \), \( \frac{1}{q} = 0.1 - 0.05 = 0.05 \), \( q = 20 \, \text{cm} \)
Magnification: \( m = -\frac{20}{20} = -1 \)
F-number: \( f/\# = \frac{10}{5} = 2 \)
Result: \( f = 10 \, \text{cm}, q = 20 \, \text{cm}, m = -1, f/\# = 2 \)

5. Frequently Asked Questions (FAQ)

Q: What does negative magnification mean?
A: It indicates an inverted image.

Q: Why is \( r_2 \) negative?
A: Due to the negative sign convention for radius to the right of center.

Q: Where to find lens parameters?
A: Refer to lens specifications or optical design data.