# Cartesian sign convention for spherical mirrors

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In this short piece of article, we will discuss the cartesian sign convention for spherical mirrors. So let’s get started…

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## Cartesian sign convention for spherical mirrors

Here are the sign conventions commonly used in the Cartesian sign convention for spherical mirrors:

### Principal axis

The central line passing through the vertex (V) of the mirror is considered the reference line for all measurements.

### Nature of distance measured

• All distances are measured from the pole of the mirror.
• All distances measured in the direction of the incident ray is taken as positive.
• All the distance measured in the direction opposite of the incident ray is taken as negative.

### Object distance (u)

• Positive when the object is on the same side as the incident light and the light rays are traveling toward the mirror.
• Negative when the object is on the opposite side as the incident light and the light rays are converging toward the mirror.

### Image distance (v)

• Positive when the image is on the same side as the outgoing light and the light rays are diverging away from the mirror.
• Negative when the image is on the opposite side as the outgoing light and the light rays are converging toward the mirror.

### Focal length (f)

• For a concave mirror, the focal length is considered negative, indicating that the focal point is located on the same side as the incident light.
• For a convex mirror, the focal length is considered positive, indicating that the focal point is located on the opposite side as the incident light.

### Object height (hₒ)

• Positive when the object is above the principal axis.
• Negative when the object is below the principal axis.

### Image height (hᵢ)

• Positive when the image is above the principal axis.
• Negative when the image is below the principal axis.

These sign conventions, when applied consistently, allow for accurate calculations and analysis of optical systems involving spherical mirrors.

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