Thin Lens Equation

📊 intermediate

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

Relates focal length, object distance, and image distance for thin lenses.

Variables & Units

$f$

Focal length

Unit: $\text{m}$

$d_o$

Object distance

Unit: $\text{m}$

$d_i$

Image distance

Unit: $\text{m}$

Key Information

📐 Derived From

Gaussian optics and paraxial approximation

💡 Example

Converging lens $f=10\,\text{cm}$, object at $d_o=30\,\text{cm}$: $1/d_i = 1/10 - 1/30 = 0.1 - 0.0333 = 0.0667$, so $d_i = 15\,\text{cm}$.

🔧 Applications

Cameras, eyeglasses, microscopes

⚠️ Constraints

Thin lens, paraxial rays, small angles

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