Light – Reflection and Refraction
Spherical mirrors
Find the images formed by concave and convex mirrors.
The two laws of reflection:
- the angle of incidence equals the angle of reflection;
- the incident ray, the normal and the reflected ray all lie in one plane.
Both angles are measured from the normal (the line at 90° to the mirror), not from the mirror. A ray making 30° with the mirror makes 60° with the normal.
"Which plane?" Not the mirror. Imagine a sheet of paper standing upright on the mirror, exactly where the ray hits. The incident ray, the normal and the reflected ray all lie flat on that one sheet.
A plane mirror gives an image that is virtual (the rays only seem to meet behind the mirror), erect, the same size, as far behind the mirror as the object is in front, and laterally inverted (left and right swapped). That is why AMBULANCE is painted back-to-front on the van: the driver in front reads it the right way in the mirror.
A spherical mirror is a small piece cut from a big hollow ball. Look at a shiny steel spoon: if the reflecting surface curves inwards, like the inside of the spoon, it is a concave mirror; if it bulges outwards, like the back of the spoon, it is a convex mirror. Its key points:
| Term | Means |
|---|---|
| Pole (P) | the centre of the mirror's surface |
| Centre of curvature (C) | the centre of the ball it was cut from |
| Radius of curvature (R) | the radius of that ball |
| Principal axis | the line through P and C |
| Principal focus (F) | where rays parallel to the axis meet (concave) or seem to come from (convex) |
| Focal length (f) | the distance from P to F |
For small mirrors, R = 2f: F lies halfway between P and C.
To find an image, draw any two of these rays from the top of the object. Notice that the first two are each other's reverse:
- parallel to the axis → passes through F (or seems to come from F);
- through F → comes out parallel to the axis;
- through C → comes straight back along itself;
- to the pole P → reflects at an equal angle on the other side.
Concave mirror: move the object closer step by step and watch the image (Table 9.1):
| Object at | Image at | Image is |
|---|---|---|
| Infinity | F | real, inverted, very small |
| Beyond C | between F and C | real, inverted, smaller |
| C | C | real, inverted, same size |
| Between C and F | beyond C | real, inverted, larger |
| F | infinity | real, inverted, very large |
| Between P and F | behind the mirror | virtual, erect, larger |
The last case is the odd one out, and the one questions love.
A convex mirror is simpler: wherever the object is, the image is virtual, erect and smaller, behind the mirror between P and F.
Uses:
- concave: torches and car headlights (bulb at F gives a strong parallel beam), shaving and dentists' mirrors (object between P and F gives a big upright image), solar furnaces (sunlight gathered at F);
- convex: the side mirrors of cars. They always give an upright image and show a wider view of the traffic behind.
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