Lens & Mirror Equation Calculator – Optics Made Easy
Calculate focal length, object distance, or image distance using the lens/mirror equation with this interactive physics tool.
Object Distance (dₒ)
cm
Image Distance (dᵢ)
cm
Focal Length (f)
cm
Result
Using equation: 1/f = 1/dₒ + 1/dᵢ
Focal Length (f) = 20 cm
Image is real and inverted.
Ray diagram for a convex lens with object beyond 2F. Image is real, inverted, and reduced.
How to Use the Calculator
- Select the quantity you want to calculate (f, dₒ, or dᵢ) from the dropdown in the left panel.
- Enter the other two known values in the input fields.
- Choose the appropriate optical element (lens or mirror type).
- Select your preferred units (cm or m).
- Click "Calculate" or the result will update automatically.
- Review the result and check the ray diagram for visualization.
Understanding the Results
The lens/mirror equation relates the focal length (f), object distance (dₒ), and image distance (dᵢ):
1/f = 1/dₒ + 1/dᵢ
Sign conventions are important in optics:
- Positive image distance (dᵢ): Real image (formed on the opposite side of the lens)
- Negative image distance (dᵢ): Virtual image (formed on the same side as the object)
- Positive focal length (f): Converging lens or concave mirror
- Negative focal length (f): Diverging lens or convex mirror
Example Calculations
Click on any example to load it into the calculator:
| Scenario | Object Distance (dₒ) | Image Distance (dᵢ) | Focal Length (f) |
|---|---|---|---|
| Convex lens, object beyond 2F | 30 cm | 60 cm | 20 cm |
| Concave lens, virtual image | 15 cm | -30 cm | -10 cm |
| Convex lens, object at 2F | 20 cm | 20 cm | 10 cm |
| Concave mirror, object beyond C | 40 cm | 13.33 cm | 10 cm |
| Convex mirror, virtual image | 0.5 m | -0.2 m | -0.33 m |