Concave Mirror Equation Calculator

What is the Concave Mirror Equation?

The concave mirror equation, also known as the mirror equation or spherical mirror equation, is a fundamental formula in optics that relates the object distance, image distance, and focal length of a concave mirror. It allows us to determine the position and characteristics of images formed by concave mirrors, which are essential in various optical systems and applications.

Formula

The concave mirror equation is expressed as:

\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]

Where:

• \( f \) is the focal length of the concave mirror (in cm or m)
• \( u \) is the object distance from the mirror (in cm or m)
• \( v \) is the image distance from the mirror (in cm or m)

Calculation Steps

Let's calculate the image distance for an object placed in front of a concave mirror:

1. Given:
   • Focal length (\( f \)) = 20 cm
   • Object distance (\( u \)) = 30 cm
2. Rearrange the equation to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \]
3. Substitute the known values: \[ \frac{1}{v} = \frac{1}{20} - \frac{1}{30} \]
4. Perform the calculation: \[ \frac{1}{v} = 0.05 - 0.0333 = 0.0167 \]
5. Solve for \( v \): \[ v = \frac{1}{0.0167} \approx 60 \text{ cm} \]

Example and Visual Representation

Let's visualize the concave mirror and the formation of an image:

This diagram illustrates:

• The concave mirror surface (blue curve)
• The principal axis (green line)
• The center of curvature C (red dot)
• The object O (yellow dot)
• The image I (gray dot)
• The ray path from object to image (dashed line)