New Cartesian Sign Convention in Optics – Rules and Examples
Sign Convention Of Lens And Mirror is a foundational concept in JEE Main Physics that determines how we assign positive and negative values to distances in optical calculations. Correctly using sign convention helps you avoid errors in mirror formula and lens formula problems, enabling smooth progress in ray diagrams and numericals involving concave and convex surfaces.
In optics, every measurement—whether object distance, image distance, or focal length—must follow an agreed set of rules to standardise results. The New Cartesian Sign Convention forms the foundation for solving questions, and it’s essential to apply it consistently across mirrors and lenses. Many students confuse sign rules for concave, convex, and plane surfaces; this page clarifies it all, focusing on JEE-level requirements.
What Is the Sign Convention in Lenses and Mirrors?
The sign convention in lenses and mirrors uses the Cartesian axis system for assigning the sign of all focal lengths, object distances (u), image distances (v), and radii of curvature (R). All distances are measured from the optical center (for lenses) or pole (for mirrors).
- Distances measured to the left of the origin (opposite to incident light) are negative.
- Distances to the right of the origin (along the direction of incident light) are positive.
- Heights measured upwards from principal axis are positive; downwards are negative.
- These conventions apply equally to both lenses and mirrors.
Remember, the sign convention is essential for correctly substituting values in the mirror formula and lens formula:
- Mirror formula: 1/v + 1/u = 1/f
- Lens formula: 1/v – 1/u = 1/f
Sign Convention Of Lens And Mirror: Detailed Rules
Applying the sign convention for lenses and mirrors in JEE numericals relies on identifying the type of surface and light direction. Below is a summary table that you can rely on for quick reference while solving optics problems:
| Quantity | Condition | Sign for Mirror | Sign for Lens |
|---|---|---|---|
| Object Distance (u) | Real object (left) | Negative | Negative |
| Image Distance (v) | Real image (left of lens/mirror) | Negative | Negative |
| Image Distance (v) | Virtual image (right of lens/behind mirror) | Positive | Positive |
| Focal Length (f) | Concave mirror or concave lens | Negative | Negative |
| Focal Length (f) | Convex mirror or convex lens | Positive | Positive |
| Radius of Curvature (R) | Center of curvature left (concave) | Negative | Negative |
| Radius of Curvature (R) | Center of curvature right (convex) | Positive | Positive |
For both mirrors and lenses, pay special attention to the sign of u, v, and f based on your ray diagram and the direction you measure from the pole/optical center.
Comparing Mirror vs. Lens Sign Conventions
The core difference between sign convention for lenses and mirrors in JEE Main lies in the position of object, image, and direction of light. In both, distances measured toward incoming light are negative. But remember these contrasts:
- For mirrors, object is usually left of pole; for lenses, object is left of optical center.
- Convex lens and convex mirror both have positive focal length.
- Concave lens and concave mirror both have negative focal length.
- Always check if your image is real/virtual based on the side of formation.
- The formula sign for object distance in lens is consistent with the mirror rule.
To further clarify, see the difference between mirror and lens and practical ray examples in your JEE revision.
Application of Sign Convention Of Lens And Mirror in JEE Problems
JEE Main numericals demand error-free use of sign convention for both images and objects. Here’s a quick solved example:
- A concave mirror with focal length f = –15 cm. An object is placed at u = –30 cm. Find image distance v.
Using the mirror formula: 1/v + 1/u = 1/f
1/v = 1/f – 1/u = (1/–15) – (1/–30) = –2/30 + 1/30 = –1/30
So, v = –30 cm (the image forms on same side as object—real image).
Always double-check the signs of u, v, f before solving, and practice similar scenarios using the optics important questions and optics mock test to reinforce these sign rules.
For a convex lens: f = +10 cm, u = –20 cm. Lens formula: 1/v – 1/u = 1/f → 1/v = 1/f + 1/u = (1/10) + (1/20) = (2+1)/20 = 3/20 ⇒ v = 6.67 cm (right of lens, so real image). The positive answer shows image is on same side as emerging rays—be sure to apply these rules consistently.
- Sign convention errors are a leading cause of mistakes in JEE optics questions.
- Draw the principal axis and mark direction of incident light; this keeps your signs correct.
- Review the sign convention in optics page for extra solved problems and error analysis.
- For practice, use lens formula and its applications and combination of mirrors resources on Vedantu.
By mastering the sign convention of lens and mirror, you tackle every JEE Main optics question—right from simple ray diagrams to tough numericals—without confusion. For faster reference and revision, always keep the main conventions table handy, and check out Vedantu’s interactive guides for more diagram-based practice.
FAQs on Sign Convention of Lens and Mirror: Explained for JEE & Boards
1. What is the sign convention of a mirror?
Sign convention of a mirror refers to the rules used to assign positive and negative signs to various distances in mirror formulas in Physics.
- All distances are measured from the pole of the mirror (the optical centre).
- Distances measured towards the incident light (usually to the left of the mirror) are considered negative.
- Distances measured in the direction of the reflected light (to the right) are considered positive.
- Focal length (f) is negative for concave mirrors and positive for convex mirrors.
2. What is the sign convention for lens?
Sign convention for lens is based on the New Cartesian Sign Convention used in optics for solving lens formula numericals.
- All linear distances are measured from the optical centre of the lens.
- Distances measured in the direction of the incident light are considered positive.
- Distances measured opposite to the incident light are negative.
- Focal length (f) is positive for convex lens, and negative for concave lens.
3. Is the sign convention for mirror and lens the same?
The sign convention for mirrors and lenses follows a similar New Cartesian rule, but their physical application differs:
- Both use the optical centre or pole as the reference point.
- For mirrors, incident light is usually from left and is considered negative.
- For lenses, incident light travels from left to right and forward directions are positive.
- The sign of focal length switches: negative for concave mirror and lens, positive for convex types.
4. What is the rule of sign convention for convex lens?
The sign convention for a convex lens is:
- The object distance (u) is negative (since object is usually placed to the left).
- Focal length (f) is taken as positive.
- The image distance (v) is positive if formed on the right side (real image), negative if on the same side as the object (virtual image).
5. Why is using the wrong sign in optics formulas problematic?
Using the wrong sign in optics formulas leads to incorrect calculation of image position, size, and nature.
- You might get negative answers for distances that should be positive, or vice versa.
- It may also result in physically impossible outcomes (e.g., image forming on the wrong side).
- To score marks in JEE, NEET, and board exams, sign errors must be avoided by following the New Cartesian Sign Convention.
6. What are the New Cartesian sign convention rules in optics?
The New Cartesian sign convention in optics includes:
- The reference point is the optical centre for lenses, and pole for mirrors.
- Directions towards incoming light (left of the optical centre) are negative.
- Directions in which light travels (right of optical centre) are positive.
- All heights above the principal axis are considered positive, below are negative.
7. How do you assign positive and negative signs for object distance in a concave mirror?
For a concave mirror (using New Cartesian sign convention):
- Object distance (u) is always negative since the object is placed to the left of the pole (opposite to the direction of reflected light).
- The reference is the pole of the mirror.
8. What is the sign of the focal length for a convex mirror?
Focal length (f) of a convex mirror is always positive according to the New Cartesian sign convention.
- Because the focus is behind the mirror (to the right of the pole), which is the positive direction.
9. What is the importance of sign convention for JEE and board exams?
The sign convention is crucial in JEE Main, NEET, and board exams because:
- It avoids sign errors in numerical answers.
- Ensures correctness in applying mirror and lens formulas.
- Allows systematic solving of ray diagrams and practical optics problems.
10. Do sign conventions change if I solve in a different direction for the ray?
No, the sign conventions do not change with the drawing direction of the ray.
- Always measure distances with respect to the fixed reference (pole or optical centre) and along the principal axis.
- The direction of light propagation and principal axis determines positive/negative, not the order in which you draw the diagram.
