E. Physics: Light and Geometric Optics · Light and Geometric OpticsOptical Instruments: Cameras, Telescopes, Microscopes and More
E1.2 E3.6 A1.3 A1.7 A2.1 A2.2About 75 minutes
Learning goals- I can explain how cameras, telescopes, binoculars and microscopes use lenses and mirrors to form images.
- I can calculate the magnification of a telescope and of a compound microscope.
- I can explain how retroreflectors and solar ovens work.
- I can assess the impact of an optical technology on society and the environment, citing reliable sources.
Words to know
objective lens
The lens nearest the object in a telescope or microscope; it forms the first image.
eyepiece
The lens you look through; it magnifies the image formed by the objective.
refracting telescope
A telescope that uses lenses to collect and focus light.
reflecting telescope
A telescope that uses a concave mirror to collect and focus light.
compound microscope
A microscope with two converging lenses: an objective and an eyepiece.
retroreflector
A device that reflects light back towards its source.
aperture
The adjustable opening that controls how much light enters a camera.
CCD (charge-coupled device)
A light sensor that turns an image into electrical signals, pixel by pixel.
Seeing farther, smaller and safer
How do we see a galaxy billions of light-years away, a single cell in a drop of pond water, or a deer on a dark highway? Every optical device in this lesson is built from the same two ingredients you have studied: mirrors and lenses. In this lesson you will explain how cameras, telescopes, binoculars, microscopes, retroreflectors and solar ovens work, and assess their impact on society and the environment.
Cameras
A camera works much like the eye. A converging lens forms a real, inverted, smaller image on a light sensor (or, in older cameras, on film). To focus on objects at different distances, the camera moves the lens slightly closer to or farther from the sensor (the eye changes the lens shape instead). An adjustable opening called the aperture controls how much light enters, like the pupil.
Most digital cameras once used a sensor called a CCD (charge-coupled device), which turns light into electric signals pixel by pixel. The CCD was invented in 1969 by Willard Boyle, a physicist born in Amherst, Nova Scotia, and George Smith. They shared the 2009 Nobel Prize in Physics for it with Charles Kao, who was honoured for his work on optical fibres. Today many cameras, including phone cameras, use a related sensor called a CMOS sensor. CCDs are still used in many scientific and astronomical cameras.
Worked exampleExample 1: Focusing a camera
A camera lens has a focal length of 50 mm. How far from the sensor must the lens be to focus on (a) a person 5.0 m away, (b) a flower 0.50 m away?
- Use 1/f = 1/dₒ + 1/dᵢ with all distances in millimetres.
- (a) dₒ = 5000 mm: 1/dᵢ = 1/50 − 1/5000 = 0.0198, so dᵢ = 50.5 mm.
- (b) dₒ = 500 mm: 1/dᵢ = 1/50 − 1/500 = 0.0180, so dᵢ = 55.6 mm.
(a) 50.5 mm, (b) 55.6 mm. To focus on closer objects, the lens moves farther from the sensor.
Refracting telescopes
A refracting telescope uses two converging lenses:
- The objective lens has a long focal length. It collects light from a distant object and forms a real, inverted image at its focal point.
- The eyepiece has a short focal length. It acts as a magnifying glass, letting you view that image up close.
The image you see is inverted, which is fine for looking at stars and planets. The magnification of a telescope is:
magnification = fₒ ÷ fₑ
A large objective lens also gathers more light, so fainter objects become visible.
A refracting telescope (thin-lens model). Parallel rays from a distant star enter the objective, meet at its focal point to form a real, inverted image, and leave the eyepiece parallel again but at a steeper angle: the object looks bigger. Here fₒ ÷ fₑ = 330 ÷ 75 = 4.4×, and the exit rays are 4.4 times steeper than the incoming rays.Worked exampleExample 2: Telescope magnification
A telescope has an objective with a focal length of 900 mm and an eyepiece with a focal length of 25 mm. Find the magnification and the approximate length of the telescope.
- Magnification = fₒ ÷ fₑ = 900 mm ÷ 25 mm = 36.
- The lenses are about fₒ + fₑ apart: 900 mm + 25 mm = 925 mm.
36×, and the telescope is about 93 cm long.
Reflecting telescopes
Large lenses are heavy, sag under their own weight, and bend different colours by different amounts. So most big research telescopes are reflecting telescopes: a large concave (parabolic) mirror collects the light and brings it to a focus, where a smaller mirror sends it to an eyepiece or a camera.
The James Webb Space Telescope, launched in December 2021, has a 6.5 m primary mirror made of 18 gold-coated hexagonal segments. Canada, through the Canadian Space Agency, contributed the telescope's Fine Guidance Sensor (which keeps it pointed precisely) and the NIRISS science instrument. In return, Canadian astronomers receive a share of observing time on the telescope.
Binoculars
Binoculars are two small telescopes side by side. A telescope's image is upside down, so each side contains prisms that use total internal reflection to flip the image right side up. The prisms also fold the light path back and forth, so binoculars can be much shorter than a telescope with the same magnification. Binoculars are labelled with two numbers, such as 8 × 42: 8× magnification, and objective lenses 42 mm across.
Compound microscopes
A compound microscope also uses two converging lenses, but here the object is very close:
- The objective lens has a very short focal length. The specimen is placed just outside its focal point, so it forms a real, inverted, enlarged image inside the tube.
- The eyepiece magnifies that image again. The first image sits inside the eyepiece's focal length, so you see a virtual, enlarged image.
Total magnification = objective magnification × eyepiece magnification
A compound microscope (thin-lens model, drawn to scale). The objective forms a real, enlarged, inverted image (image 1). The eyepiece acts as a magnifier for image 1, producing a large virtual image (dashed) that your eye sees. Here the objective magnifies 4× and the eyepiece about 2.7×, for a total of about 11×; real microscopes use much stronger lenses.Worked exampleExample 3: Total magnification
A microscope has a 10× eyepiece and objectives of 4×, 10× and 40×. What is the greatest total magnification?
- Total magnification = objective × eyepiece.
- The greatest uses the 40× objective: 40 × 10 = 400.
400×: a cell 0.01 mm wide appears 4 mm wide.
Retroreflectors and solar ovens
A retroreflector sends light straight back towards its source, no matter what angle it comes in at. A corner reflector uses mirrors (or, in 3-D, three surfaces) at right angles to each other: each reflection reverses part of the ray's direction. Bicycle reflectors, the reflective strips on safety vests, and many highway signs use tiny corner reflectors or glass beads so that a driver's headlights light them up brightly for the driver.
In 1969, the Apollo 11 astronauts left a panel of corner-cube retroreflectors on the Moon. Scientists on Earth still bounce laser pulses off it and time their return to measure the distance to the Moon very precisely.
A solar oven (solar cooker) uses shiny reflectors to concentrate sunlight onto a dark cooking pot. A parabolic solar cooker is a concave mirror: parallel rays from the Sun are reflected through its focal point, where the pot sits. Solar cookers need no fuel and produce no smoke, which makes them useful where firewood is scarce.
A 2-D corner reflector: two plane mirrors at 90°. Each ray reflects twice (following the law of reflection) and leaves travelling exactly opposite to the way it came in, back towards the source.Just for funLight-speed Moon check: a laser pulse sent to the Apollo 11 reflector travels about 384 000 km each way. At 3.00 × 10⁸ m/s, the round trip takes about 2.6 seconds. By timing these pulses, scientists have found that the Moon is slowly moving away from Earth, by about 3.8 cm per year, roughly the rate at which your fingernails grow!
Assessing impacts (E1.2)
When you assess an optical technology, consider benefits and costs for society and the environment:
- Medicine: microscopes made it possible to see bacteria and cells, transforming the diagnosis of disease. Endoscopes (bundles of optical fibres) let doctors see inside the body without major surgery. Femtosecond lasers, which rely on chirped pulse amplification developed by Donna Strickland (born in Guelph, Ontario) and Gérard Mourou, are used in eye surgery.
- Science: telescopes changed our understanding of our place in the universe.
- Safety: retroreflectors make cyclists and pedestrians visible at night.
- Environment: solar cookers reduce the need to cut firewood and reduce indoor smoke. Satellite cameras monitor forests, ice and wildlife. But manufacturing electronics uses energy and materials, and discarded devices add to electronic waste.
- Privacy: cheap, powerful cameras and drones raise questions about privacy and surveillance.
Research and citing sources (A1.3, A1.7)
For an assessment project, look for reliable sources: government agencies (such as the Canadian Space Agency or NASA), universities, science museums and peer-reviewed articles. Record each source's author, title, date, publisher and web address as you go, and use a consistent citation style (such as APA or MLA). Put ideas in your own words and give credit for the ones that are not yours.
Hands-on activityBuild a simple telescope
You need: two magnifying glasses (or one magnifying glass and a lens from old +3 D reading glasses), a ruler, tape, and a paper towel tube or rolled-up poster paper.
- Find the focal length of each lens: on an overcast day or in a room, focus the image of a distant window or lamp onto a sheet of paper and measure the lens-to-paper distance. (Do not use the Sun.)
- The lens with the longer focal length is the objective; the one with the shorter focal length is the eyepiece.
- Hold the eyepiece near your eye and the objective in front of it, about fₒ + fₑ apart. Look at a distant tree or building and slide the objective until the image is sharp. Tape the lenses into the tube at that spacing.
- Is the image upright or inverted? Predict the magnification using fₒ ÷ fₑ, then compare by looking at a brick wall with one eye through the telescope and the other eye open.
What to look for: the image is inverted and enlarged, and the lenses end up about fₒ + fₑ apart.
Safety (grown-up note): Never point a telescope, binoculars or any lens towards the Sun, and never look at the Sun through any optical device: it can cause permanent eye damage in an instant. Do not leave lenses in direct sunlight, where they can focus light and start a fire. Handle glass lenses carefully; their edges can chip.
Your turn
1What kind of image does a camera lens form on the sensor?
Real, inverted and smaller than the object.
2A telescope has fₒ = 1200 mm and fₑ = 20 mm. Find the magnification.
3Why do binoculars contain prisms?
To flip the image right side up and fold the light path (by total internal reflection) so binoculars are shorter.
4A microscope uses a 10× eyepiece and a 40× objective. Find the total magnification.
5Why does a bicycle reflector look bright to a driver whose headlights shine on it?
It is a retroreflector: it sends the light back towards its source, the car, so the driver sees it brightly.
6Where should the pot sit in a parabolic solar cooker? Why?
At the focal point, where the reflected sunlight is concentrated.
More practice: warm-up
1Which lens in a telescope has the longer focal length?
2What does the number 42 mean on 8 × 42 binoculars?
The objective lenses are 42 mm across.
3Name the Canadian who co-invented the CCD.
4What type of mirror collects light in a reflecting telescope?
A concave (parabolic) mirror.
5Is the image you see in a compound microscope real or virtual?
Virtual (and enlarged, inverted).
More practice: on your own
1A camera with a 35 mm lens focuses on an object 2.0 m away. How far is the lens from the sensor?
1/dᵢ = 1/35 − 1/2000 = 0.02807, so dᵢ ≈ 35.6 mm.
2You want 50× magnification with a 25 mm eyepiece. What focal length objective do you need?
fₒ = 50 × 25 mm = 1250 mm.
3Give two reasons large research telescopes use mirrors rather than lenses.
Large lenses are heavy and sag (can only be supported at the edges), and lenses bend colours differently, blurring images; a mirror can be supported from behind and reflects all colours the same way.
4Explain why the specimen must be just outside the objective's focal point in a microscope.
An object outside F of a converging lens forms a real image; when it is between F and 2F, the image is enlarged. That image is then magnified again by the eyepiece.
5Assess one positive and one negative impact of widespread cameras on society.
Positive: for example, security, medical imaging, documenting events, scientific research. Negative: for example, loss of privacy, surveillance, and electronic waste.
Challenge
1A telescope is 51 cm long (fₒ + fₑ) and has a magnification of 50×. Find fₒ and fₑ.
fₒ = 50 fₑ, so 51 fₑ = 51 cm: fₑ = 1.0 cm and fₒ = 50 cm.
2In the microscope figure, the objective (f = 40) has the specimen at 50. Use the thin lens equation to find the image distance and magnification of the objective.
1/dᵢ = 1/40 − 1/50 = 1/200, so dᵢ = 200 and M = −200/50 = −4 (4× larger, inverted).
3Evaluate solar cookers as a technology for communities that depend on firewood. Use at least three criteria.
Benefits: no fuel cost, less deforestation, no smoke (better health), no carbon emissions from burning. Limits: work only in sunny weather and during the day, cook more slowly, need sunlight safety (concentrated light can burn skin and eyes). Judgement: a useful complement to other cooking methods, especially in sunny regions.
Check your understandingQuiz
1. The objective lens of a refracting telescope has:
2. A telescope with fₒ = 800 mm and fₑ = 20 mm has a magnification of:
3. Total magnification of a microscope with a 10× eyepiece and a 4× objective:
4. Binoculars use prisms mainly to:
5. A retroreflector sends light:
6. Willard Boyle shared a Nobel Prize for inventing:
7. To focus on a closer object, a camera lens moves:
For parents and teachersBig idea: Expectations E1.2 and E3.6 ask students to explain how mirrors and lenses are used in optical instruments, and to assess the social and environmental impact of devices that use light. Every instrument here combines ideas from earlier lessons: concave mirrors, converging lenses and total internal reflection.
Common difficulties:
- Mixing up telescope and microscope objectives. A telescope objective has a long focal length (distant objects); a microscope objective has a very short one (very close objects).
- Adding instead of multiplying magnifications in a microscope.
- Assessing: students should weigh benefits and costs and support a judgement, not just list facts.
How to help: If you have binoculars, a camera or a magnifying glass at home, take them apart (in thought) together: which part forms the image? Look at road signs and bike reflectors at night from a car: they shine back towards the headlights. Safety: never let anyone point binoculars, a telescope or a lens at the Sun.