1. What is the Convex Mirror Equation?

The convex mirror equation, \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \), relates the focal length (f), image distance (v), and object distance (u) for convex mirrors. This equation is fundamental in geometric optics.

2. How Does the Calculator Work?

The calculator uses the mirror equation:

Where:

• \( f \) — Focal length (positive for convex mirrors)
• \( v \) — Image distance (virtual image, negative value)
• \( u \) — Object distance (positive value)

Explanation: The equation shows the relationship between these three variables. You can calculate any one variable if you know the other two.

3. Importance of Mirror Equation

Details: This equation is crucial for understanding image formation in convex mirrors, which are used in various applications like vehicle side mirrors, security mirrors, and optical instruments.

4. Using the Calculator

Tips: Enter any two known values (f, v, or u) to calculate the third. Remember that for convex mirrors, focal length is positive, image distance is negative, and object distance is positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is image distance negative for convex mirrors?
A: The negative sign indicates that the image is virtual (appears to be behind the mirror) and upright.

Q2: What is the sign convention for convex mirrors?
A: Focal length (f) is positive, object distance (u) is positive, and image distance (v) is negative.

Q3: How does image size relate to these values?
A: The magnification (m) is given by m = -v/u, which is always positive and less than 1 for convex mirrors.

Q4: What are typical uses of convex mirrors?
A: They're used in vehicle side mirrors, security mirrors in stores, and at blind corners because they provide a wider field of view.

Q5: How does this differ from concave mirror equations?
A: The same equation applies, but sign conventions differ - concave mirrors have positive focal length and image distance can be positive or negative.