1. What is the Lens/Mirror Formula?

The lens/mirror formula relates the focal length (f), image distance (v), and object distance (u) for lenses and mirrors. It's a fundamental equation in geometric optics that helps determine the relationship between these three quantities.

2. How Does the Calculator Work?

The calculator uses the lens/mirror equation:

Where:

• \( f \) — Focal length (m)
• \( v \) — Image distance (m)
• \( u \) — Object distance (m)

Explanation: The equation shows the inverse relationship between the focal length and the difference of the reciprocals of the image and object distances.

3. Sign Convention

Details:

• For lenses: f is positive for convex lenses, negative for concave lenses
• For mirrors: f is positive for concave mirrors, negative for convex mirrors
• v is positive for real images, negative for virtual images
• u is always negative (as per Cartesian sign convention)

4. Using the Calculator

Tips: Enter any two known values (f, v, or u) to calculate the third unknown value. All values should be in meters.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between lens and mirror formulas?
A: The formula is the same, but the sign conventions differ for lenses and mirrors.

Q2: Can this be used for both concave and convex lenses/mirrors?
A: Yes, but remember to use the correct sign convention for each case.

Q3: What units should I use?
A: The calculator uses meters (m) for all distances. Convert from cm by dividing by 100.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for thin lenses and spherical mirrors in the paraxial approximation.

Q5: What if I get a negative result?
A: Negative values have physical meaning in optics - they indicate virtual images, diverging lenses, or convex mirrors.