Lenses redirect light to form images, while prisms separate white light into colours. Together they explain cameras, spectacles, telescopes, rainbows, and why different wavelengths of light do not all bend by the same amount.
Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.
Why can a diamond sparkle so strongly, and why does white light split into colours in a prism or rainbow instead of staying as one single beam?
Type your prediction below. You will revisit it at the end.
Write your prediction in your book. You will revisit it at the end.
Wrong: Momentum is not conserved in collisions with friction.
Right: Momentum is always conserved in isolated systems; friction is an external force, so the system must include the surface.
📚 Core Content
A convex lens converges parallel rays, while a concave lens causes them to diverge. The shape of the lens determines how light is redirected at each surface.
A converging (convex) lens is thicker at the centre than at the edges. When parallel rays enter the lens, they are refracted toward the principal axis and converge at the focal point on the far side. This focal point is real — light actually passes through it. A diverging (concave) lens is thinner at the centre. Parallel rays spread out as if they originated from a virtual focal point on the same side as the incoming light.
The optical centre is the middle of the lens. A ray passing straight through the optical centre is not deviated because the two surfaces are effectively parallel at that point. The principal axis is the line passing through the optical centre perpendicular to the lens faces. Every lens diagram is built around this axis.
| Feature | Converging (convex) | Diverging (concave) |
|---|---|---|
| Shape | Thicker in the middle | Thinner in the middle |
| Effect on parallel rays | Converge toward focal point | Diverge from virtual focal point |
| Focal length sign | Positive (+f) | Negative (−f) |
| Typical image | Real or virtual depending on object distance | Always virtual, upright, reduced |
Lens diagrams rely on a small set of predictable rays. If you can draw these three rays accurately, you can locate the image for any object position.
For a converging lens, the three special rays are:
For a diverging lens, the rules are similar but the focal point is virtual:
Where the refracted rays (or their backward extensions) intersect is the image location. If the intersection is on the opposite side of the lens from the object, the image is real. If it is on the same side, the image is virtual.
Ray diagrams show the geometry; the thin lens equation gives the numerical position and size of the image.
The thin lens equation relates the object distance $d_o$, image distance $d_i$, and focal length $f$:
The magnification $m$ tells you how large the image is compared with the object and whether it is inverted:
Sign conventions matter. For a converging lens, $f$ is positive. For a diverging lens, $f$ is negative. A positive $d_i$ means the image is real and on the opposite side of the lens from the object. A negative $d_i$ means the image is virtual and on the same side as the object. If $m$ is negative, the image is inverted; if $m$ is positive, it is upright. These equations are especially useful when the ray diagram is hard to scale accurately.
White light separates into colours because the refractive index of a material depends slightly on wavelength. This is why a prism produces a spectrum and why rainbows arc across the sky.
When light enters a transparent medium such as glass or water, its speed decreases. The amount of bending (refraction) depends on how much the speed changes, which is described by the refractive index $n = c/v$. For most transparent materials, violet light (shorter wavelength, ~400 nm) experiences a slightly higher refractive index than red light (longer wavelength, ~700 nm). Because violet light slows down more in the medium, it bends more sharply at each interface.
When white light passes through a prism, it undergoes two refractions — once entering the glass and once leaving. Each colour bends by a slightly different angle, spreading the beam into a spectrum from red (least bent) to violet (most bent). The same principle operates in rainbows: sunlight enters a water droplet, refracts, reflects off the back of the droplet, and refracts again as it exits. The double refraction inside the droplet separates the colours, and millions of droplets collectively form the rainbow arc.
Light intensity from a point source follows the inverse square law, just like sound intensity. As light spreads out spherically from a source, the same total energy is distributed over an ever-larger surface area.
At distance $r$ from a point source, the light passes through a sphere of surface area $4\pi r^2$. Because the same total power is spread over this area, the intensity $I$ at distance $r$ is:
This means intensity is proportional to $1/r^2$. If the distance from the source doubles, the area increases by a factor of 4, so the intensity becomes one quarter. If the distance triples, the intensity drops to one ninth. This matters in brightness comparisons, lighting design, photography exposure, and any context where light spreads out from a source.
Lenses and dispersion show up across everyday technology and natural phenomena. Understanding both allows you to explain why optical devices are designed the way they are.
Cameras use converging lenses to focus light onto a sensor. The lens moves closer to or farther from the sensor to focus on objects at different distances. Microscopes use two converging lenses — the objective forms a real, enlarged image, and the eyepiece acts as a magnifying glass to enlarge that image further. Telescopes use a large objective lens to collect as much light as possible and form a real image, which is then magnified by the eyepiece.
Spectacles correct vision problems: convex lenses for long-sightedness (converging light before it reaches the eye) and concave lenses for short-sightedness (diverging light so it focuses farther back). Chromatic aberration in camera lenses occurs because different colours focus at slightly different points — lens designers combine multiple elements made of different glasses to cancel this out. This is called an achromatic doublet.
Visual Break — Decision Flowchart
✏️ Worked Examples
Problem type: Type 16 — Thin lens equation with sign conventions.
Scenario: A convex lens has focal length 12 cm and an object is placed 18 cm from the lens. Find the image distance and the magnification. State whether the image is real or virtual, upright or inverted.
If the object were moved inside the focal length to do = 8 cm, predict the sign of di before calculating. Then use the thin lens equation to confirm whether the image becomes virtual and upright.
Problem type: Type 16 — Light intensity and distance.
Scenario: Light intensity is measured as 80 units at 2 m from a point source. Find the intensity at 4 m and at 6 m.
At what distance would the intensity fall to 5 units? Show the rearrangement and solve for the new distance.
🏃 Activities
| Device | Lens / optical idea | Your one-sentence explanation |
|---|---|---|
| Magnifying glass | ||
| Camera | ||
| Short-sighted spectacles | ||
| Telescope | ||
| Prism spectrum |
Type your matched answers and explanations below.
Complete the table in your book with the lens idea and explanation for each device.
Type your calculated check and image description below.
Draw the diagram in your book and write the image description and calculation check.
Earlier you were asked why white light splits into colours and why diamonds can sparkle so strongly.
The full answer: different wavelengths of light refract by different amounts because refractive index depends on wavelength. White light separates into a spectrum through dispersion. Diamond has an exceptionally high refractive index and a small critical angle, so light undergoes multiple internal reflections and strong dispersion, producing dramatic flashes of colour known as fire.
Now revisit your prediction. What role does wavelength play in the splitting of white light?
Annotate your prediction in your book with what you now understand differently.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
✅ Check Your Understanding
1. A convex lens is best described as:
2. For a converging lens, a ray through the optical centre travels:
3. Dispersion occurs because:
4. In a prism, which colour refracts more strongly?
5. If distance from a point light source doubles, intensity becomes:
6. A concave lens typically forms an image that is:
7. Explain the difference between a converging lens and a diverging lens. 3 MARKS
8. A convex lens has focal length 10 cm and object distance 15 cm. Find the image distance. 3 MARKS
9. Explain what dispersion is and why a rainbow shows violet and red in different directions. 4 MARKS
1. A — a convex lens is converging.
2. D — a ray through the optical centre continues undeviated.
3. B — dispersion occurs because refractive index varies slightly with wavelength.
4. C — violet refracts more strongly than red.
5. A — doubling distance reduces intensity to one quarter.
6. B — a concave lens forms a virtual, upright, reduced image.
Activity 1 — Lens Application Match:
Activity 3 — Brightness Comparison:
(1) I2 = 120 × (3/6)² = 120 × 1/4 = 30 units
(2) I3 = 120 × (3/9)² = 120 × 1/9 = 13.3 units
(3) Intensity is spread over the surface area of a sphere (4πr²). When distance doubles, the surface area quadruples, so the same total power is spread over four times the area. Therefore intensity falls to one quarter, not one half.
Q7 (3 marks): A converging (convex) lens refracts parallel rays so that they move toward each other and may meet at a focal point. It can form real or virtual images depending on the object distance. A diverging (concave) lens refracts parallel rays so that they spread out as if they came from a virtual focal point. It always forms a virtual, upright, reduced image.
Q8 (3 marks): Use $1/f = 1/d_o + 1/d_i$. So $1/10 = 1/15 + 1/d_i$, giving $1/d_i = 1/10 - 1/15 = 3/30 - 2/30 = 1/30$. Therefore $d_i = 30$ cm. The image is real because $d_i$ is positive.
Q9 (4 marks): Dispersion is the separation of white light into its component colours because different wavelengths refract by slightly different amounts. Violet light has a shorter wavelength and experiences a larger refractive effect than red light, so it bends more strongly. In a rainbow, sunlight undergoes refraction, reflection, and a second refraction inside water droplets. The double refraction separates the colours, causing violet and red to emerge in different directions.
Tick when you have finished the activities and checked the answers.