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**SIGN CONVENTION FOR LENSES**

A **lens**** **is a curved surface that causes the light rays falling on it to either converge or diverge. The sign convention is a set of rules that determine the signs of the parameters associated with a lens. Consider a lens having radii of curvatures as R_{1} and R_{2} corresponding to the surfaces S_{1} and S_{2} respectively.

The sign of R_{1} and R_{2} depends on the shape of the surfaces constituting the lens. We can say,

R_{1}>0 if S_{1} is convex

R_{1}<0 if S_{1} is concave

R_{2}>0 if S_{2} is concave

R_{2}<0 if S_{2} is convex

We can tabulate the **sign convention of the radii of curvatures of the two surfaces of a lens** as:

Type of Lens | R_{1} | R_{2} |

Biconvex | R_{1 }> 0 | R_{2}_{ }< 0 |

Diverging Meniscus | R_{1 }> 0 | R_{2}_{ }> 0 |

Converging Meniscus | R_{1} < 0 | R_{2}_{ }< 0 |

Biconcave | R_{1} < 0 | R_{2}_{ }> 0 |

Plano-concave | R_{1} = ∞ | R_{2}_{ }> 0 |

Plano-convex | R_{1} = ∞ | R_{2}_{ }< 0 |

Plano-concave | R_{1}_{ }< 0 | R_{2} = ∞ |

Plano-convex | R_{1} = ∞ | R_{2} = ∞ |

**Lens sign convention table:**

Quantity | Condition | Sign |

Focal Length | Convex Lens Concave Lens | Positive (+) Negative (-) |

Object Distance | Always | Negative (-) |

Image Distance | Real Image Virtual Image | Positive (+) Negative (-) |

Magnification | Upright Image Upturn Image | Positive (+) Negative (-) |