Study Guides/Physics/Sign Convention
Study Guide · Physics

Sign Convention for Spherical Mirrors and Lenses

In Class 10 Physics (Light: Reflection and Refraction), solving numerical problems is impossible without strictly following the New Cartesian Sign Convention. It tells us when to use a positive (+) or negative (-) sign for distances.

Question (Click to Flip)

Why is the object distance (u) always negative?

Answer

According to the sign convention, we always place the object in front of the mirror/lens (on the left side). Since distances to the left of the pole are measured against the direction of incident light, 'u' is always taken as negative.

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Key Facts

If the magnification (m) calculated is negative, it guarantees that the image is Real and Inverted. If (m) is positive, the image is Virtual and Erect.

The Basic Rules (The Origin)

Imagine a standard X-Y graph. The pole (P) of the mirror or the optical centre (O) of the lens is considered the Origin (0,0).

  1. Object Placement: The object is ALWAYS placed on the left side of the mirror/lens. Therefore, light always falls from left to right.
  2. X-Axis (Horizontal Distances):
    • All distances measured to the Right of the pole are taken as Positive (+).
    • All distances measured to the Left of the pole are taken as Negative (-).
  3. Y-Axis (Heights):
    • Heights measured Upwards (above the principal axis) are Positive (+).
    • Heights measured Downwards (below the principal axis) are Negative (-).

Summary of Signs (Crucial for Numericals)

  • Object Distance (u): ALWAYS Negative (-).
  • Object Height (h): ALWAYS Positive (+).

Focal Length (f):

  • Convex Mirror / Convex Lens: ALWAYS Positive (+).
  • Concave Mirror / Concave Lens: ALWAYS Negative (-).

Image Distance (v) & Height (h'):

  • Real and Inverted image: v is negative (for mirrors), h' is negative.
  • Virtual and Erect image: v is positive (for mirrors), h' is positive.

Questions and Answers

Why is the object distance (u) always negative?+

According to the sign convention, we always place the object in front of the mirror/lens (on the left side). Since distances to the left of the pole are measured against the direction of incident light, 'u' is always taken as negative.

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