Reflection of Light in Curved Mirrors
Senior 2 · Physics
Reflection of Light in Curved Mirrors
Lesson 2 of 4
25 min
Stand far from a shiny concave mirror and your image is small and upside down; walk towards it and the image grows, flips and finally appears huge and upright behind the mirror. A ray diagram lets you predict exactly where the image will be and what it will look like for any object position. It is also one of the most reliable sources of marks in a physics exam.
From the top of the object, draw any two of these rays. Where the reflected rays meet (or appear to meet) is the top of the image.
| Incident ray | Concave mirror: reflected ray | Convex mirror: reflected ray |
|---|---|---|
| 1. Parallel to the principal axis | Passes through F | Appears to come from F (behind the mirror) |
| 2. Through F (concave) or aimed at F (convex) | Returns parallel to the axis | Returns parallel to the axis |
| 3. Through C (concave) or aimed at C (convex) | Returns back along itself | Returns back along itself |
| 4. To the pole P | Reflects at the same angle on the other side of the axis | Reflects at the same angle on the other side of the axis |
Draw real rays as solid lines and extensions behind the mirror as dashed lines. Draw a real image as a solid arrow and a virtual image as a dashed arrow.
Move an object from far away towards a concave mirror, and the image changes like this:
| Object position | Image position | Nature of the image | Example use |
|---|---|---|---|
| At infinity (very far away) | At F | Real, inverted, very diminished (a point) | Solar cooker, telescope |
| Beyond C | Between F and C | Real, inverted, diminished | Forming a small, real image on a screen |
| At C | At C | Real, inverted, same size | Finding the radius of curvature in the lab |
| Between C and F | Beyond C | Real, inverted, magnified | Projector |
| At F | At infinity | No clear image: the reflected rays are parallel | Torch and headlamp reflectors |
| Between F and P | Behind the mirror | Virtual, upright, magnified | Shaving and make-up mirrors, dentists' mirrors |
Worked example. A candle stands 15 cm in front of a concave mirror of focal length 10 cm (so C is at 20 cm). The candle is between C and F, so the table predicts a real, inverted, magnified image beyond C. A careful scale drawing (1 square = 5 cm) with ray 1 (parallel, then through F) and ray 3 (through C, back along itself) shows the rays crossing about 30 cm in front of the mirror, below the axis, with the image twice as tall as the candle. The next lesson shows how to get the same answer by calculation.
Wherever the object is placed, a convex mirror always forms an image that is virtual, upright and diminished, located behind the mirror between P and F. As the object moves closer, the image grows a little but never becomes larger than the object. Because the mirror bulges outward, it collects light from a very wide area: this wide field of view is its great advantage.
Open Geometric Optics and choose the Mirror screen. Select a concave mirror and show the principal rays. Drag the object from far away, past C and F, to very close to the mirror, and compare what you see with the table above. Then switch to a convex mirror and check that the image is always upright, smaller and behind the mirror.
Tip
Describe an image with three words, every time: real or virtual; inverted or upright; magnified, diminished or same size. Then give its position.
Pick the easiest two rays: "parallel → through F" and "through C → straight back" are the quickest to draw accurately with a ruler.
An object is placed beyond C in front of a concave mirror. Describe the image.
Solution: Between F and C; real, inverted and diminished.
Where must an object be placed in front of a concave mirror to give a real image the same size as the object?
Solution: At C (a distance of 2f from the mirror). The image is also at C, inverted.
Keza holds a concave mirror close to her face and sees a large, upright image. Where is her face relative to F, and is the image real or virtual?
Solution: Her face is between F and the pole. The image is virtual (behind the mirror), upright and magnified.
A car is 10 m behind a moto whose side mirror is convex. Describe the image the rider sees.
Solution: Virtual, upright and diminished, behind the mirror between P and F. (That is why the car looks further away than it really is.)
Why can a real image be caught on a screen but a virtual image cannot?
Solution: At a real image the light rays actually meet, so a screen placed there receives the light. A virtual image is where rays only appear to come from, behind the mirror, and no light actually reaches that place.
Remember
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