Predicting Images with Principal Rays in Concave and Convex Mirrors

Hello again. In the previous lesson, you learned to extract information from sound-wave diagrams: amplitude indicates loudness, while frequency indicates pitch. This lesson uses the same assessment skill in a different setting: read the features of a diagram carefully, then make a justified conclusion.

Now we turn to principal-ray diagrams for curved mirrors. By the end, you should be able to draw the key rays and use their paths to identify an image’s position, size, orientation, and whether it is real or virtual.

---

The language of curved-mirror diagrams

A curved mirror is usually drawn as a small part of a sphere. The horizontal line through its middle is the principal axis. In assessment diagrams, an upright arrow represents the object; its top is usually the point from which you draw rays.

Three labelled points matter:

• Vertex, $V$: the middle of the mirror’s reflecting surface.
• Focal point, $F$: the point associated with rays parallel to the principal axis.
• Centre of curvature, $C$: the centre of the sphere of which the mirror is part.

For a concave mirror, $F$ and $C$ are in front of the mirror, on the same side as the object. The focal point lies halfway between $V$ and $C$, so:

$$VC=2VF$$

A concave mirror curves inward, like the inside of a spoon. It is a converging mirror: reflected rays can meet in front of it.

A convex mirror bulges outward, like the back of a spoon. It is a diverging mirror: reflected rays spread out after reflection.

The two types of image are crucial:

• A real image forms where light rays actually meet. It is on the same side of the mirror as the object and can be projected onto a screen.
• A virtual image forms where reflected rays only appear to come from. It is located behind the mirror, cannot be projected onto a screen, and is found by extending rays backward using dashed lines.

---

The principal rays for a concave mirror

You only need two rays from the top of the object to locate its image. Draw them accurately with a ruler.

For a concave mirror, use these rules:

1. A ray that travels parallel to the principal axis reflects through $F$.
2. A ray that travels through $F$ on its way to the mirror reflects parallel to the principal axis.

There is also a useful third ray:

3. A ray directed through $C$ hits the mirror at right angles and reflects back along the same path.

The first two are normally fastest. Their reflected paths either meet in front of the mirror or, if they diverge, appear to meet behind it once extended backward.

How to construct the diagram

Use this reliable drawing routine every time:

1. Draw the principal axis, mirror, and labels $F$ and $C$.
2. Draw the object as an arrow with its base on the principal axis.
3. From the top of the object, draw one incident ray parallel to the axis.
4. Reflect that ray through $F$.
5. Draw a second incident ray from the top through $F$.
6. Reflect that second ray parallel to the axis.
7. Find the intersection of the reflected rays. This is the top of the image.
8. Draw the image arrow from the principal axis to that point.

Use solid lines for real reflected rays. If rays are diverging, continue them behind the mirror using dashed lines only. The dashed extensions show where the rays appear to originate; light does not actually travel behind the mirror.

A good written conclusion does not merely say “the image is there.” State all four characteristics:

The image forms between $C$ and $F$, is real, inverted, and smaller than the object.

---

Predicting images with a concave mirror

The position of the object relative to $F$ and $C$ determines the result. The ray diagram is the evidence; this table helps you check what your completed drawing should show.

Object position	Image position	Size	Orientation	Type
Beyond $C$	Between $C$ and $F$	Smaller	Inverted	Real
At $C$	At $C$	Same size	Inverted	Real
Between $C$ and $F$	Beyond $C$	Larger	Inverted	Real
At $F$	No finite image position	—	—	—
Between $F$ and the mirror	Behind the mirror	Larger	Upright	Virtual

There is a pattern worth understanding rather than memorising mechanically.

When the object is farther than $F$ from a concave mirror, the reflected rays converge and cross. The image is therefore real and inverted. As the object moves closer to $F$, the image moves farther away from the mirror and becomes larger.

When the object is inside $F$, the reflected rays spread apart instead of crossing. Extend them backward: their extensions meet behind the mirror. The image is therefore virtual, upright, and magnified. This is the principle of a concave shaving or make-up mirror.

At exactly $F$, reflected rays are parallel. Since they never meet at a finite position, assessments usually describe this as no image formed or an image at infinity.

The most frequent concave-mirror errors are:

• Drawing a parallel incident ray and reflecting it through $C$, rather than through $F$.
• Forgetting that a real image is inverted.
• Treating a virtual image as though rays physically meet behind the mirror.
• Reversing the image position for an object beyond $C$: the image must be closer to the mirror, between $C$ and $F$.

---

Convex mirrors: same method, different outcome

Convex-mirror ray diagrams use the same basic method, but the focal point and centre of curvature are behind the mirror. Since the reflecting surface bulges towards the object, reflected rays always diverge.

The two principal-ray rules are:

1. A ray parallel to the principal axis reflects outward. Its backward dashed extension passes through $F$.
2. A ray directed towards $F$ reflects parallel to the principal axis.

In the second rule, remember that the ray does not reach $F$: $F$ lies behind the mirror. You draw the incident ray in the direction of $F$, stopping it when it reaches the mirror.

For a convex mirror, follow the same drawing procedure as before:

1. From the top of the object, draw a ray parallel to the principal axis.
2. Reflect it away from the mirror so that its dashed extension passes through $F$.
3. Draw another incident ray towards $F$.
4. Reflect that ray parallel to the principal axis.
5. Extend both reflected rays backward with dashed lines.
6. The point where the dashed lines cross is the top of the image.

Unlike concave mirrors, convex mirrors have only one outcome for an ordinary object in front of them:

Mirror	Image position	Size	Orientation	Type
Convex	Behind the mirror, between $V$ and $F$	Smaller	Upright	Virtual

This is why convex mirrors are used as vehicle side mirrors and security mirrors: they make objects look smaller but show a wider field of view.

---

Reading an unfamiliar ray diagram

In an assessment, you may be given a completed ray diagram rather than asked to draw one. Work from the ray paths, not from guesswork.

If the reflected solid rays meet

The image is:

• at their intersection,
• real,
• on the object side of the mirror,
• usually inverted for a concave mirror.

Compare the height of the image arrow with the object arrow to decide whether it is larger, smaller, or the same size.

If reflected rays spread apart

Look for dashed extensions behind the mirror. The image is:

• where those extensions meet,
• virtual,
• behind the mirror,
• upright.

For a convex mirror, the image is also always reduced. For a concave mirror with the object inside $F$, it is enlarged.

A useful way to organise your answer is L-S-O-T:

Letter	Ask yourself
L: Location	Where is the image relative to $F$, $C$, and the mirror?
S: Size	Is the image larger, smaller, or equal in size?
O: Orientation	Is it upright or inverted?
T: Type	Is it real or virtual?

For example:

The object is between $C$ and $F$ of a concave mirror. The reflected rays meet beyond $C$, so the image is real and inverted. The image arrow is taller than the object arrow, so it is enlarged.

That explanation identifies visible diagram evidence and connects it directly to the conclusion.

---

Final assessment checklist

Before handing in a ray-diagram question, check:

• Is the mirror correctly identified as concave or convex?
• Have you labelled $F$, $C$, and the principal axis correctly?
• Did your rays begin at the top of the object?
• For a concave mirror, did the parallel ray reflect through $F$?
• For a convex mirror, did you use dashed backward extensions through $F$?
• Did you use a ruler and add arrowheads to show light direction?
• Have you stated location, size, orientation, and type?

---

Key takeaways

Principal-ray diagrams let you predict an image by tracing just two carefully chosen rays.

• A concave mirror can form real, inverted images when the object is beyond $F$, or a virtual, upright, enlarged image when the object is inside $F$.
• A convex mirror always forms an image that is virtual, upright, smaller, and behind the mirror between $V$ and $F$.
• Solid rays actually travel along their paths; dashed lines are backward extensions used to find virtual images.
• In any response, describe the image using location, size, orientation, and type.

You have now covered both diagram skills in this assessment-practice module: interpreting sound waves and using ray diagrams for curved mirrors.