Ch 4 · 3.2.3 Thin Lenses · O Level Physics 5054
Topic 4 of 7 in Waves — O Level Physics 5054 — 71 lessons.
Introduction
A magnifying glass, a camera, a projector, your own eye and the glasses that correct it all use lenses. A lens is a shaped piece of glass or plastic that refracts light to make an image. This lesson shows how to predict where that image forms, by drawing three simple rays. (Syllabus section 3.2.3.)
Key ideas — Two kinds of thin lens
🧑🏫 Teacher's explanation
Think of a lens as a tool that redirects light rays. A converging lens is like a crowd of people all walking towards a single narrow doorway; the rays are 'pushed' together until they meet at a single point. A diverging lens is like a crowd walking away from a single point; the rays are 'pushed' apart, appearing to originate from a point behind the lens.
📖 Definitions
🔍 Worked example — Easy
An object of length 2.0 cm is viewed through a magnifying glass. The image formed has a length of 6.0 cm. Calculate the linear magnification.
🔍 Worked example — Standard
A converging lens is used to create a real image. If the distance from the principal focus to the lens is 15 cm, what is the focal length of the lens?
🔍 Worked example — Exam-style
A student uses a magnifying glass to view a small insect. The insect is 5 mm long. The image seen through the lens is 25 mm long. Calculate the linear magnification.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Calculate the linear magnification produced by the lens. [2] (b) State whether the image formed is real or virtual. [1] [3 marks]
Key ideas — Key terms
There is a principal focus on each side of a lens, at the same distance. A fatter (more curved) lens bends light more and has a shorter focal length.
🧑🏫 Teacher's explanation
Think of a lens as a tool that 'redirects' light. A converging lens (like a magnifying glass) acts like a funnel, bringing parallel light rays together to a single point. A diverging lens (like the ones used to fix near-sightedness) acts like a spreader, taking parallel rays and pushing them apart.
📖 Definitions
🔍 Worked example — Easy
An object of height 2.0 cm is placed in front of a magnifying glass. The image formed has a height of 6.0 cm. Calculate the linear magnification.
🔍 Worked example — Standard
A converging lens has a focal length of 15 cm. A beam of parallel light rays enters the lens. How far from the lens will the rays meet on the principal axis?
🔍 Worked example — Exam-style
A student uses a single lens as a magnifying glass. The object is 5.0 cm from the lens. The lens has a focal length of 10 cm. Determine if the image formed is real or virtual.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Calculate the linear magnification of the lens. [2] (b) State whether the image is real or virtual. [1] [3 marks]
Key ideas — Drawing ray diagrams for a converging lens
Draw the object as an upright arrow standing on the principal axis. Use any two of these three rays from the top of the object:
🧑🏫 Teacher's explanation
Imagine a magnifying glass. When you hold it far from a page, the letters look upside down and large; this is because the light rays actually cross each other after passing through the lens. When you bring it very close to the page, the letters look upright and huge; this is because the light rays are spreading apart, and your eye has to 'trace them back' to see where they seem to come from.
📖 Definitions
🔍 Worked example — Easy
An object of height 2.0 cm is placed in front of a converging lens. The image formed is 6.0 cm tall. Calculate the linear magnification.
🔍 Worked example — Standard
A student uses a magnifying glass to view a specimen. The specimen is 5.0 cm tall and the image seen through the lens is 25 cm tall. Calculate the magnification.
🔍 Worked example — Exam-style
An object is placed 15 cm from a converging lens with a focal length of 10 cm. Determine if the image is real or virtual and calculate its magnification. (Assume the image is real).
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Where the image forms (converging lens)
🧑🏫 Teacher's explanation
Think of a converging lens as a 'light gatherer' that forces rays to meet at a specific point. Imagine you are holding a magnifying glass under a bright sun; the lens bends the sunlight toward a single, intense point. This point is where the light 'wants' to go.
📖 Definitions
🔍 Worked example — Easy
An object of height 2.0 cm is placed 15 cm from a converging lens with a focal length f = 10 cm. Calculate the height of the image.
🔍 Worked example — Standard
A magnifying glass has a focal length of 5.0 cm. An insect is placed 2.0 cm from the lens. Calculate the linear magnification.
🔍 Worked example — Exam-style
An object 5.0 cm tall is placed 30 cm from a converging lens. The image formed is 15 cm tall. Calculate the linear magnification.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Linear magnification
linear magnification = image length/object length
🧑🏫 Teacher's explanation
Imagine you are looking at a tiny ant through a magnifying glass. The ant looks much larger to your eye than it actually is. This 'enlargement factor' is what we call linear magnification. It tells us how many times bigger the image appears compared to the actual object.
📖 Definitions
🔍 Worked example — Easy
An object of height 2.0 cm is placed in front of a magnifying glass. The image formed has a height of 10 cm. Calculate the linear magnification.
🔍 Worked example — Standard
A lens produces an image that is 0.5 cm tall. If the linear magnification is 0.25, calculate the height of the actual object.
🔍 Worked example — Exam-style
An object is placed in front of a converging lens. The image formed is 15 mm tall. The object is 45 mm tall. Calculate the linear magnification and state whether the image is an enlargement or a reduction.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Calculate the linear magnification of the image. [2] (b) State whether the image is an enlargement or a reduction. [1] [3 marks]
Key ideas — The magnifying glass
Hold a converging lens so that the object is closer to the lens than the focal length. The rays leaving the lens diverge; your eye traces them back to a larger, upright, virtual image behind the object.
🧑🏫 Teacher's explanation
Think of a magnifying glass as a 'trickster' for your eyes. When you look at something through a lens, your eye doesn't see the object itself; it sees the light rays coming from it. If the light rays are traveling perfectly straight, your eye thinks the object is right there. But if the lens bends those rays so they spread apart (diverge), your brain follows those lines backward to a point much further away and much larger.
📖 Definitions
🔍 Worked example — Easy
An object of height 2.0 cm is placed in front of a magnifying glass. The lens produces an image that is 6.0 cm tall. Calculate the linear magnification.
🔍 Worked example — Standard
A converging lens has a focal length of 10 cm. An object is placed 5 cm from the lens. Describe the nature of the image formed (size and orientation) and state whether it is real or virtual.
🔍 Worked example — Exam-style
An object 4.0 cm high is placed 15 cm from a converging lens with a focal length of 10 cm. Calculate the height of the image.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — The eye
The eye's cornea and lens focus light to form a real, inverted, diminished image on the retina at the back of the eye. The brain turns the image the right way up.
Practical notes
Worked example
Example 1: magnification. An object 2.0 cm tall gives an image 6.0 cm tall.
🔍 Worked example — Easy
An object with a height of 2.5 cm is placed in front of a lens. The resulting image has a height of 7.5 cm. Calculate the linear magnification.
🔍 Worked example — Standard
A converging lens has a focal length of 15 cm. An object 45 cm from the lens is 5.0 cm tall. Calculate the height of the image formed.
🔍 Worked example — Exam-style
A magnifying glass uses a converging lens with a focal length of 5.0 cm. An object is placed 3.0 cm from the lens. Determine if the image is real or virtual, and calculate its magnification.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) The distance from the centre of the lens to the principal focus, where rays parallel to the principal axis meet after passing through the lens. (2) Virtual, upright and magnified; a magnifying glass. (3) 1.5 / 6.0 = 0.25. (4) Short sight; the image of a distant object forms in front of the retina; a diverging lens.