1. What is the Mirror Equation?

The mirror equation relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror. It is fundamental in geometric optics for determining the position of images formed by mirrors.

2. How Does the Calculator Work?

The calculator uses the mirror equation:

Where:

• \( u \) — Object distance from mirror (m)
• \( v \) — Image distance from mirror (m)
• \( f \) — Focal length of the mirror (m)

Explanation: The negative sign indicates that the object distance is measured opposite to the direction of incoming light (real objects have negative distances in the sign convention).

3. Importance of Object Distance Calculation

Details: Calculating object distance is essential for designing optical systems, understanding image formation, and predicting the characteristics (real/virtual, upright/inverted, magnified/reduced) of images formed by mirrors.

4. Using the Calculator

Tips: Enter image distance (v) and focal length (f) in meters. Both values must be non-zero, and v cannot equal f (which would make the denominator zero).

5. Frequently Asked Questions (FAQ)

Q1: What sign convention is used in this calculator?
A: The calculator uses the Cartesian sign convention where distances measured against the direction of incoming light are negative.

Q2: How does the focal length affect the result?
A: For concave mirrors (f positive), the equation gives real object positions. For convex mirrors (f negative), it gives virtual object positions.

Q3: What happens when v = f?
A: The equation becomes undefined as the denominator becomes zero, which corresponds to the case where the object is at infinity.

Q4: Can this be used for both concave and convex mirrors?
A: Yes, the equation works for both types of spherical mirrors when used with the proper sign convention.

Q5: What units should I use?
A: The calculator uses meters, but any consistent unit can be used as long as all inputs are in the same unit.