Question
What image is formed for different object positions in concave and convex mirrors? Summarise all cases with image characteristics.
Solution — Step by Step
The three standard rays for mirrors
To draw any ray diagram, we need two of these three rays:
- Parallel ray: Incident ray parallel to principal axis reflects through the focus (F)
- Focal ray: Incident ray passing through F reflects parallel to the principal axis
- Centre ray: Incident ray directed toward the centre of curvature (C) reflects back on itself
Where any two reflected rays meet = image location.
Concave mirror — 6 object positions
| Object Position | Image Position | Nature | Size |
|---|---|---|---|
| At infinity | At F | Real, inverted | Point-sized |
| Beyond C | Between F and C | Real, inverted | Diminished |
| At C | At C | Real, inverted | Same size |
| Between C and F | Beyond C | Real, inverted | Magnified |
| At F | At infinity | Real, inverted | Highly magnified |
| Between F and P (pole) | Behind mirror | Virtual, erect | Magnified |
The pattern: as the object moves from infinity toward F, the image moves from F toward infinity and grows larger. Once the object passes F (between F and pole), the image flips to virtual and appears behind the mirror.
Convex mirror — always one case
No matter where we place the object, a convex mirror always forms an image that is:
- Behind the mirror (between P and F)
- Virtual and erect
- Diminished
As the object moves closer, the image grows slightly larger but never becomes magnified (at maximum, it approaches the size of the object when the object is at the mirror surface).
This is why convex mirrors are used as rear-view mirrors — they always show an upright, smaller image with a wide field of view.
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Why This Works
The mirror formula governs all cases:
Sign convention (New Cartesian): distances measured from the pole. Direction of incident light is positive. For a concave mirror, is negative; for a convex mirror, is positive.
Magnification:
If is negative, the image is inverted (real). If is positive, the image is erect (virtual).
Alternative Method
Instead of memorising 6 cases, use the mirror formula directly:
- Put (object distance, negative for real objects in concave mirror) and into the formula
- Solve for
- Check the sign of : negative = real image (in front), positive = virtual (behind)
- Calculate : magnitude gives size, sign gives orientation
This approach works for any object distance, including fractional positions — no memorisation needed.
💡 Expert Tip
For CBSE boards (Class 10), drawing the ray diagram is mandatory for full marks. Always draw at least two of the three standard rays. For JEE/NEET, the formula-based approach is faster, but understanding the ray diagram helps catch sign errors.
Common Mistake
⚠️ Common Mistake
The most common sign convention error: students use positive values for concave mirror focal length. In the New Cartesian convention (used in CBSE, NEET, JEE), the focal length of a concave mirror is negative and that of a convex mirror is positive. Using the wrong sign gives an image on the wrong side. Always draw a quick diagram to verify your sign convention before solving.