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Lesson 7 of 7

Light: Mirrors and Lenses · Lesson 7 of 7

Chapter Summary and Practice

“Connect the whole chapter through a quick recap, comparisons, worked revision, and mixed practice.”

Learning Objectives

• Connect mirror and lens shape with their effects on light and images. • Apply both reflection laws and distinguish angles measured from a mirror and its normal. • Predict broad image changes when object distance changes. • Choose optical devices for viewing, monitoring, and solar-heating purposes. • Interpret diagrams and explain observations using evidence rather than memorised names.

What we have studied

Begin by recalling the journey through the chapter. We first identified surfaces, then observed images, investigated reflection laws, and followed beams through mirrors and lenses. Use this table as a quick route back to the six lessons. If a row feels unfamiliar, revisit that lesson before attempting the mixed questions.

LessonWhat we studiedWhat you should now be able to explain
What Are Spherical Mirrors?Plane, concave, and convex surfaces; spoon observations; mirror symbols; shape and coatingIdentify the reflecting face and distinguish a shape model from real manufacture
Images Formed by Spherical MirrorsImage size, orientation, distance changes, lateral reversal, mirror usesCompare image patterns and explain dental and wide-view uses
What Are the Laws of Reflection?Rays, normal, point of incidence, i = r, same-plane law, normal incidenceTrace reflection, use the correct angle reference, and explain the two experiments
How Mirrors Converge and Diverge LightParallel reflected beams, concentration of sunlight, solar applicationsExplain why concave mirrors gather light and convex mirrors spread it
What Is a Lens, and How Does It Change an Image?Lens shape, water-drop lens, distance-dependent images, pencil-through-water observationIdentify lenses and distinguish an altered image from a changed object
How Lenses Converge and Diverge LightParallel transmitted beams, sunlight concentration, instruments, eye lensCompare lenses with mirrors and connect lens behaviour to applications

One comparison connects the optical devices

Keep three questions separate: What shape has the surface or lens? Does the useful light reflect back or pass through? What image or beam pattern results? The shared words concave and convex do not by themselves tell you the effect. This comparison brings together the main observations without introducing new formulas.

DeviceIdentifying featureImage of an ordinary objectInitially parallel beam
Plane mirrorFlat reflecting faceErect and same-sizeReflected rays remain parallel
Concave mirrorInward-curving reflecting faceClose enough: erect and enlarged; suitable farther positions: inverted, with varying sizeReflected rays converge
Convex mirrorOutward-bulging reflecting faceErect and diminishedReflected rays diverge
Convex lensMiddle thicker than edgesClose enough: erect and enlarged; suitable farther positions: inverted, with varying sizeTransmitted rays converge
Concave lensMiddle thinner than edgesErect and diminishedTransmitted rays diverge
Thin flat glass plateFlat transparent surfacesNo obvious lens-like magnification in the source comparisonOutgoing rays remain approximately parallel

A concave mirror and a convex lens share a gathering effect, but one uses reflection and the other transmission. Their useful nearby enlarged views also depend on arranging the object appropriately. A convex mirror and a concave lens share upright diminished images of ordinary objects, but their surface shapes and light paths are different.

Reflection: check the normal first

The normal is perpendicular to the mirror at the point where light strikes. Both i and r are measured from it, and they are equal. The incident ray, reflected ray, and normal at that point also lie in one plane. At normal incidence, i = r = 0° and the ray returns along its incoming line. Tilting a mirror changes its normal, not the laws.

Reflection relationshipLaTeX
i and r are the angles of incidence and reflection, measured from the local normal.
Example — Switch the angle reference

Problem
The incident ray makes 40° with the normal. Find the reflected ray’s angle with the mirror.

  1. 1.The angle of incidence is 40°, so the angle of reflection is 40°.
  2. 2.The normal is perpendicular to the mirror, making a 90° angle with it.
  3. 3.The reflected ray therefore makes 90° − 40° = 50° with the mirror.
A: along the normalB: tilted, along normalC: tilted, 20° to normali = r = 0°i = r = 0°i = r = 20°
Normal incidence and a tilted mirror— The rays return along their incoming line in A and B. In C, the incoming and outgoing rays make equal angles with the tilted normal.

Recognise image patterns, not just names

An image observation may identify a device, but some observations are shared. “Upright and smaller” fits a convex mirror or a concave lens, so you must also know whether you are looking in a reflector or through a transparent lens. A sequence of observations is especially helpful for identifying a concave mirror or convex lens.

ABCReference spacingReduced spacingEnlarged spacingFor an enlarged upright concave-mirror view, the graph must be suitably close.
Grid spacing as image-size evidence— These are schematic upright image samples. Larger, smaller, and unchanged grid spacing provide evidence about magnification.
Example — Identify and justify

Problem
A mirror gives an upright enlarged image nearby and an inverted image farther away. Another mirror always gives an upright smaller image. Identify them.

  1. 1.The first device is a mirror, so compare mirror image patterns rather than lens shapes.
  2. 2.An enlarged upright image that changes to inverted fits a concave mirror.
  3. 3.An image that stays upright and diminished fits a convex mirror. Confirm the identification by observing each reflecting curve.
AOMIBOMICOMIO = object; M = mirror; I = observed image. Arrows compare relative sizes.
Match mirrors to image sizes— All three objects have the same size. Identify the mirror consistent with each image at the shown suitable viewing arrangement. Positions are schematic.
AObjectImageBObjectImageCObjectImageTransparent devices at suitable close object distances: compare sizes.
Match a lens or flat glass to its image— One arrangement enlarges the upright object, one diminishes it, and one keeps the comparison size. Identify convex lens, concave lens, and flat glass.

The source also compares reflections of graph paper. An enlarged view makes grid spacing appear larger, a diminished view makes it appear smaller, and a plane-mirror view keeps the scale unchanged. With a concave mirror, specify that the graph is at a suitable close distance for an upright enlarged view. The grid pattern is evidence about image size, not about the physical paper stretching.

Connect properties with applications

Choose the optical effect that the task needs. A dentist wants a nearby enlarged view, a driver needs a wide view of traffic, and a solar receiver needs concentrated light. Torches and headlights use concave reflectors to direct light. Telescopes collect or guide light using mirrors, lenses, or both depending on the design; cameras and microscopes also use lenses. The eye lens can change shape for near and far viewing.

Example — Explain a solar receiver

Problem
Why can both a concave mirror and a convex lens be used to gather sunlight onto a small receiver?

  1. 1.Sunlight at the device is approximately parallel because the Sun is distant.
  2. 2.A concave mirror gathers reflected rays, while a convex lens gathers transmitted rays.
  3. 3.The receiver absorbs concentrated light and becomes hot. The devices redirect existing energy; they do not create it.
Quick misconception check

Concave does not always mean enlarged: concave-mirror image size depends on distance. Convex does not always mean diminished: a convex lens can magnify a nearby object. A zero reflection angle does not mean no reflection. A wider field of view does not mean larger images. An optically distorted pencil has not physically bent or thickened.

Mixed chapter quiz

These questions combine identification, angles, distance changes, and applications. If you hesitate, identify the relevant observation or optical mechanism before selecting an answer.

Quiz

Quick check

A ray is incident at 40° to the normal. The reflected ray makes what angle with the mirror?

Quick check

A ray follows the normal of a tilted mirror. Its angle of reflection is:

Quick check

In the mirror-size diagram, A is same-size, B is smaller, and C is larger and upright. Which matching is consistent?

Quick check

In the transparent-device diagram, A enlarges, B diminishes, and C gives the reference size. Which matching fits?

Quick check

A visitor walks from far away toward a concave mirror. Which broad sequence can she observe?

Quick check

Assertion: Convex mirrors are useful for observing traffic behind. Reason: They offer a wider field of view than similarly sized plane mirrors. Choose the best evaluation.

Quick check

A magnifying glass placed suitably close to text is normally a:

Quick check

Which pairing gives an erect diminished image of an ordinary object?

Quick check

The lower part of a pencil appears altered through a water-filled tumbler because:

Quick check

Which statement includes both laws of reflection?

Practice Problems

Practice Problems
  1. A ray makes 40° with the normal. Find its reflected angle with the normal and with the mirror. Then repeat when the given 40° is with the mirror instead.
  2. Draw reflected rays for three cases: incidence along a horizontal mirror’s normal; incidence along a tilted mirror’s normal; incidence at 20° to a tilted mirror’s normal. Use a protractor and state each angle of reflection.
  3. Use the mirror-size diagram to match A, B, and C to plane, convex, and concave mirrors. Explain what additional distance observation helps confirm the concave mirror.
  4. Use the transparent-device diagram to identify convex lens, concave lens, and flat glass. Explain why the observation must specify a suitable close distance.
  5. A student says that a ray along the normal has i = 90° and does not reflect. Correct both parts of the statement.
  6. A graph sheet is viewed in three mirrors. One image has unchanged grid spacing, one has reduced spacing, and one has enlarged spacing at a suitable close distance. Identify the mirror types and explain the evidence.
  7. A woman walks toward a large concave mirror from a distant position. Describe the broad sequence of changes in image size and orientation.
  8. Hold a magnifying glass above print at a suitable close distance, then move it away. Describe the image change and identify the lens type.
  9. Match each device to its distinguishing source property: concave mirror, convex mirror, convex lens, concave lens. Use inward reflecting curve; erect diminished reflected image; transmitted image that can become inverted; transmitted image that stays erect and diminished.
  10. Evaluate the traffic-mirror assertion and reason in the quiz. Also explain why the mirror warning cautions that vehicles may be closer than they appear.
  11. Draw two object–mirror–image sketches, labelling O, M, and I. In the first, the erect image is shorter than the object; in the second, it is taller. Identify the convex-mirror and close concave-mirror arrangements, using panels B and C in the mirror-size diagram as checks. Explain why image size must be interpreted with orientation and distance.
  12. Observe a pencil through a clear empty tumbler and through the same tumbler half-filled with water. Describe the lower part’s altered appearance and explain it using transmitted light, without claiming that the pencil actually changed shape.
  13. Explain how a water drop acts as a simple lens. Include why the thin oil or wax coating is used in the investigation.
  14. Compare parallel light reflected by three mirrors with parallel light passing through flat glass and two lenses. Include direction arrows and use convergence and divergence correctly.
  15. Connect the dental mirror, torch reflector, road-safety mirror, surveillance mirror, camera lens, microscope, telescope, and eye lens to the task each performs.
  16. Describe the bent-paper experiment and the historical use of water reflections for observing stars and planets. What does each contribute to understanding reflection?
  17. Choose a virtual mirror or lens simulation. Move one object through several positions while keeping the device fixed. Record size and orientation, compare the results with this chapter, and write two questions for a classmate.
  18. Review a solar-cooker proposal: check its concentrating surface, receiver position, materials, budget, sunlight limitations, and safety arrangements. Explain the energy sequence from sunlight to useful heat.

Check your reasoning after practice

A useful self-check names the observation and explains why it supports the answer. These short checks address the main source question types. They do not replace drawing and measuring your own rays or describing your actual activity observations.

For 40° to the normal, r is 40° and the reflected angle with the mirror is 50°. For 40° to the mirror, i and r are 50°. Along either horizontal or tilted normals, r is 0°. For incidence at 20° to the tilted normal, r is 20°.

Key Takeaways

Key Takeaways

• Use surface shape, reflection or transmission, image properties, and beam behaviour together to identify a device. • Reflection obeys i = r and the same-plane law; both angles use the normal as their reference. • Plane mirrors give erect same-size images; convex mirrors and concave lenses give erect diminished images of ordinary objects. • Concave mirrors and convex lenses have distance-dependent image size and orientation. • Concave mirrors and convex lenses converge suitable parallel light; convex mirrors and concave lenses diverge it. • Optical appearances do not physically change a toy, text, or pencil. • Applications depend on the purpose: enlarged detail, a wide view, guided light, or concentrated solar energy. • The eye’s lens can change shape; sunlight-concentration demonstrations require careful adult supervision.