1. What spherical mirrors are
A spherical mirror is made from a piece of a sphere. If the inside surface reflects light, it is a concave mirror. If the outside surface reflects light, it is a convex mirror.
I like to think of both types as curved mirrors whose curvature controls how they bend and spread reflected rays.
1.1. Concave and convex surfaces
Concave mirror: Curved inward like the inside of a bowl. It can make parallel rays meet at a point.
Convex mirror: Curved outward. It spreads out parallel rays as if they came from a point behind the mirror.
2. Important terms used with spherical mirrors
Whenever I deal with spherical mirrors, I use a standard set of points and distances:
- Pole (P): The midpoint of the mirror surface.
- Centre of curvature (C): The centre of the sphere of which the mirror is a part.
- Radius of curvature (R): Distance between C and P.
- Principal axis: The straight line joining P and C.
- Focus (F): The point where parallel rays either meet (concave) or appear to meet (convex) after reflection.
- Focal length (f): Distance between F and P.
3. Relation between R and f
For both concave and convex mirrors, the focal length is related to the radius of curvature by:
\( f = \dfrac{R}{2} \)
This comes from the geometry of spherical surfaces. I always remember that the focus is halfway between the pole and the centre of curvature.
4. Sign convention
To avoid confusion, a standard sign convention is used:
- Distances measured in the direction of the incident light are positive.
- Distances measured opposite to the incident light are negative.
- Heights measured upward from the principal axis are positive.
- Heights measured downward are negative.
With this convention, a concave mirror has a negative focal length, while a convex mirror has a positive focal length.
5. How concave mirrors form images
A concave mirror can form real or virtual images depending on where the object is placed. The key is how the reflected rays behave:
5.1. Parallel rays meeting at the focus
When parallel rays hit a concave mirror, they converge and meet at the focus. This property is useful for torches, headlights and solar concentrators.
5.2. Different object positions
The image changes as the object moves:
- Beyond C: Real, inverted, smaller.
- At C: Real, inverted, same size.
- Between C and F: Real, inverted, larger.
- At F: Rays become parallel; image at infinity.
- Between F and P: Virtual, upright, magnified.
6. How convex mirrors form images
A convex mirror always forms a virtual, upright and smaller image. The reflected rays diverge, and when I extend them backward, they appear to come from a point behind the mirror.
6.1. Image characteristics
- Always virtual.
- Always upright.
- Always diminished.
- Located behind the mirror.
- Formed between the pole and the focus.
6.2. Why convex mirrors are useful
Because they give a wider field of view, convex mirrors are used for vehicle side mirrors and at turns in corridors or roads.
7. Ray diagrams I usually draw
To locate the image in either concave or convex mirrors, I usually draw two principal rays:
- A ray parallel to the principal axis (passes through F for concave; appears to come from F for convex).
- A ray passing through C (reflected back along the same path).
- Or a ray passing through F (reflected parallel).
Even though many rays reflect from the mirror, two well-chosen rays are enough to find the image position.
8. Everyday places where I notice spherical mirrors
- Shaving/Makeup mirrors (concave, used for magnification).
- Vehicle headlights (concave reflectors focus the bulb's light).
- Solar cookers (concave to concentrate sunlight).
- Vehicle side mirrors (convex for wider view).
- Security mirrors in shops (large convex mirrors).