Your eye traces the reflected rays back to a point behind the mirror
Definition
Image
The point from which rays of light appear to come after they have been reflected or refracted, which is where the eye judges the object to be.
- Light spreads out from every point on the object in all directions, and some of those rays travel towards the mirror.
- Each ray reflects off the mirror obeying i=ri = ri=r, so the rays leave the mirror as a diverging (spreading) bundle.
- Your eye cannot tell that the rays have been bent, so it assumes they travelled in straight lines and traces them backwards until they meet.
- They meet at a single point behind the mirror, and that point is where you see the image.
- On a ray diagram these backward extensions are drawn as dashed lines, because no light actually travels along them.
- Doing this for the top and the bottom of the object gives two image points, and joining them gives the whole image.
The image is virtual, upright, the same size and equally far behind
Definition
Virtual image
An image formed where diverging rays are extended backwards and appear to meet, so no light actually reaches that point and the image cannot be caught on a screen.
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The image is the same size as the object, so a 15 cm15\ \text{cm}15 cm pencil has a 15 cm15\ \text{cm}15 cm image however close to the mirror you hold it.
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The image is as far behind the mirror as the object is in front, measured perpendicular to the mirror surface.
image distance=object distance \text{image distance} = \text{object distance} image distance=object distance -
The image is upright, meaning the same way up as the object, and never turned upside down.
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The image is laterally inverted, so left and right are swapped, which is why the writing on an ambulance bonnet is printed back to front.
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The image is virtual, so holding a screen behind the mirror catches nothing: the light never gets there.
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The line joining the object to its image crosses the mirror at 90∘90^\circ90∘, which is the geometric fact all the mirror constructions rely on.
Constructing the image: reflect the object in the mirror line
- Extend the mirror as a thin dashed line right across the page, so you have a line to reflect in even where the mirror itself stops.
- From each end of the object, drop a construction line perpendicular to that mirror line.
- Measure how far each end sits in front of the mirror and mark the matching point the same distance behind it.
- Join those two marked points with a dashed line, and label it as the virtual image.
- To show how an eye sees a particular point, rule a straight line from the image point to the eye, mark where it crosses the mirror, and that crossing point is where the real ray reflected.
- Draw the real ray solid with arrows from the object to the mirror and on to the eye, and leave the part behind the mirror dashed.
Practical
Investigation: locating the image in a plane mirror
- Aim: to find where the image in a plane mirror is formed, and to compare the image distance with the object distance.
- Apparatus: a plane mirror on a stand, four optical pins, a cork mat or soft board, a 30 cm30\ \text{cm}30 cm ruler, a protractor, a sharp pencil and plain paper.
- Method:
- Pin the paper to the board, rule a base line and stand the mirror with its reflecting surface exactly on it.
- Push an object pin upright into the board about 8 cm8\ \text{cm}8 cm in front of the mirror and mark its position.
- Look into the mirror from one side, well off to the left, and line up two sighting pins so that they and the image of the object pin all appear in one straight line.
- Move your head from side to side and check the pins and the image stay lined up, which shows there is no parallax between them.
- Mark both pin positions, then repeat the sighting from well over to the right to get a second pair of marks.
- Take the mirror and pins away, rule each pair of marks into a long line and extend both lines behind the base line until they cross.
- Repeat the whole thing for object distances of about 4 cm4\ \text{cm}4 cm, 8 cm8\ \text{cm}8 cm and 12 cm12\ \text{cm}12 cm.
- Measure and plot: measure the perpendicular distance of the object pin in front of the base line and of the crossing point behind it, tabulate them as object distance / cm and image distance / cm, and plot one against the other.
- Result: the lines cross behind the mirror at the position of the image, the graph is a straight line through the origin of gradient 111, and the object-to-image line meets the mirror at 90∘90^\circ90∘.
- Watch out:
- Take the two sightings from widely different angles, because two lines that cross at a shallow angle give a very uncertain crossing point.
- Keep every pin vertical, since a leaning pin lines up at the top and not at the base.
- A thick mirror reflects partly from its front glass surface, so use a thin mirror and always line up with the brighter image.
- Safety: optical pins are sharp, so push them into the board rather than the bench and collect every one at the end; handle the mirror by its edges.
Calculating distances between an object and its image
- Because the image sits the same distance behind the mirror, the object-to-image separation is twice the object distance.
- Moving the object towards the mirror by a certain distance moves the image towards the mirror by the same amount, so the gap between them closes at twice that rate.
- This is why walking towards a mirror at 1 m/s1\ \text{m/s}1 m/s makes your reflection close on you at 2 m/s2\ \text{m/s}2 m/s.
- Every distance in these calculations is measured perpendicular to the mirror, not along the slanting path the light actually takes.
Common Mistake
- Do not describe the image as inverted; it is upright, and only left and right are swapped.
- Do not say the image gets smaller as you step back, because the image is always the same size as the object.
- Do not draw the rays behind the mirror as solid lines with arrows, since no light travels there.
- Do not measure the object distance along a slanting ray; it is the perpendicular distance to the mirror.
- Do not claim a virtual image cannot be seen; you see it perfectly well, you just cannot catch it on a screen.
Exam technique
- When the question asks for the characteristics of the image, give all four: same size, same distance, upright and virtual, since each is a separate mark.
- In a construction question the position is usually accepted within a few millimetres, so measure with a ruler rather than judging by eye.
- Solid line for real light, dashed line for the extension behind the mirror, is what the drawing mark is actually testing.
- If you are asked to explain why the image is virtual, say that the reflected rays are diverging and only appear to come from behind the mirror.
- Describing the pin experiment scores for the two sightings from different angles and for the no-parallax check, so do not leave those out.
Self review
- Explain how a plane mirror forms an image, referring to what the eye does with the reflected rays.
- List four characteristics of the image formed by a plane mirror.
- What does it mean to say an image is virtual?
- An object is 30 cm30\ \text{cm}30 cm from a plane mirror. How far is it from its image?
- Describe how the no-parallax pin method is used to find the position of the image.
