Light – Reflection and Refraction · Lesson 15 of 15
Chapter Summary and Practice
“Every ray, mirror and lens returns for one final group photo.”
• Connect reflection, refraction, mirrors and lenses into one coherent picture. • Recall the important definitions and image-formation cases. • Select and apply every major optical formula correctly. • Use sign conventions to interpret image position, orientation and size. • Solve mixed conceptual and numerical problems with systematic checks.
A ray of light may return from a surface, change direction at a boundary, converge to a real image or appear to spread from a virtual one. The ideas studied across this chapter are not separate tricks. They are one connected system built from ray paths, geometry, material-dependent speed and careful sign conventions.
Core Definitions
| Term | Meaning |
|---|---|
| Reflection of light | Return of light into the same medium after it strikes a surface |
| Normal | Line perpendicular to a surface at the point of incidence |
| Real image | Image formed by the actual meeting of rays; it can be obtained on a screen |
| Virtual image | Image formed by the apparent meeting of backward ray extensions; it cannot be obtained on a screen |
| Spherical mirror | Mirror whose reflecting surface forms part of a sphere |
| Concave mirror | Spherical mirror whose reflecting surface curves inward and can converge parallel rays |
| Convex mirror | Spherical mirror whose reflecting surface bulges outward and diverges reflected rays |
| Pole P | Centre of the reflecting surface of a spherical mirror |
| Centre of curvature C | Centre of the sphere of which the mirror is a part |
| Radius of curvature R | Radius of that sphere, equal to PC |
| Principal axis | Straight line through P and C for a mirror, or through C₁ and C₂ for a lens |
| Principal focus F | Point where parallel rays meet or appear to diverge from after reflection or refraction |
| Focal length f | Distance from P or O to the principal focus |
| Aperture | Effective diameter of the reflecting surface or lens outline |
| Refraction of light | Change in direction at a boundary caused by a change in light speed |
| Lateral displacement | Sideways separation between the incident ray's original line and the parallel emergent ray from a slab |
| Refractive index | Speed ratio that measures the optical effect of a medium |
| Optical density | Comparison based on refractive index and light speed rather than mass per volume |
| Lens | Transparent material bounded by two surfaces, at least one spherical |
| Convex lens | Lens thicker at the centre that converges parallel rays |
| Concave lens | Lens thinner at the centre that diverges parallel rays |
| Optical centre O | Central point of a thin lens through which a ray passes with negligible deviation |
| Magnification m | Ratio of image height to object height; its sign indicates orientation in the adopted convention |
| Power of a lens | Reciprocal of focal length in metres |
| Dioptre | Unit of lens power; one dioptre equals one inverse metre |
Reflection and Mirrors
Reflection obeys two laws: the incidence angle equals the reflection angle, and the incident ray, reflected ray and normal lie in one plane. Both angles are measured from the normal. A plane mirror forms a virtual, erect, same-sized and laterally inverted image at the same distance behind the mirror as the object is in front.
A concave mirror converges parallel rays at a real focus in front. A convex mirror makes reflected rays diverge as though they came from a focus behind it. For small-aperture spherical mirrors, F lies midway between P and C. Concave mirrors are used when convergence or magnification is needed; convex mirrors are used when an erect image and wide field of view are more valuable.
Concave-Mirror Image Review
| Object | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F | Point-sized | Real and inverted |
| Beyond C | Between F and C | Diminished | Real and inverted |
| At C | At C | Same size | Real and inverted |
| Between C and F | Beyond C | Enlarged | Real and inverted |
| At F | At infinity | No finite screen image | Reflected rays parallel |
| Between F and P | Behind mirror | Enlarged | Virtual and erect |
Convex-Mirror Image Review
| Object | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F behind mirror | Point-sized | Virtual and erect |
| At any finite distance | Between P and F behind mirror | Diminished | Virtual and erect |
Mirror Formula and Magnification
Refraction and Refractive Index
A ray entering an optically denser medium obliquely slows and bends toward the normal. Entering an optically rarer medium, it speeds up and bends away. At normal incidence its speed changes but its direction does not. In a rectangular glass slab, equal and opposite bending at parallel faces makes the emergent ray parallel to the incident ray, though laterally displaced.
Optical density is determined by refractive index, not by mass per volume. The larger-index medium carries light more slowly. Snell's law applies to a given colour and pair of media, so reversing the direction reverses the relative index.
Lenses and Image Formation
A convex lens is thicker at the centre and converges parallel rays; a concave lens is thinner at the centre and diverges them. A lens has two centres of curvature, two principal foci and an optical centre. In the thin-lens model, a ray through O passes with negligible deviation.
Convex-Lens Image Review
| Object | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F₂ | Point-sized | Real and inverted |
| Beyond 2F₁ | Between F₂ and 2F₂ | Diminished | Real and inverted |
| At 2F₁ | At 2F₂ | Same size | Real and inverted |
| Between F₁ and 2F₁ | Beyond 2F₂ | Enlarged | Real and inverted |
| At F₁ | At infinity | No finite screen image | Emergent rays parallel |
| Between F₁ and O | Object side | Enlarged | Virtual and erect |
Concave-Lens Image Review
| Object | Image position | Size | Nature |
|---|---|---|---|
| At infinity | At F₁ | Point-sized | Virtual and erect |
| At any finite distance | Between F₁ and O | Diminished | Virtual and erect |
Lens Formula, Magnification and Power
Sign Convention Review
| Quantity | Mirror convention | Lens convention |
|---|---|---|
| Origin | Pole P | Optical centre O |
| Real object on left | u negative | u negative |
| Concave focal length | Negative | Negative |
| Convex focal length | Positive | Positive |
| Real image | v negative in front of mirror | v positive on opposite side |
| Virtual image | v positive behind mirror | v negative on object side |
| Erect image height | h′ positive | h′ positive |
| Inverted image height | h′ negative | h′ negative |
A Reliable Problem-Solving Method
- Sketch the device, object region and likely image before calculating.
- List every given quantity with its unit and Cartesian sign.
- Choose the mirror, lens, refractive-index or power formula that matches the device.
- Rearrange symbolically before inserting numbers.
- Keep distances in one unit; use metres specifically for power in dioptres.
- Interpret signs and magnitude, then compare the result with the ray-diagram prediction.
Problem
A concave mirror has f = -12 cm and an object at u = -18 cm. Find image position and magnification.
- 1.Use 1/v = 1/f - 1/u = -1/12 + 1/18.
- 2.With denominator 36, 1/v = (-3 + 2)/36 = -1/36, so v = -36 cm.
- 3.m = -v/u = -(-36)/(-18) = -2.
- 4.The image is 36 cm in front, real, inverted and twice enlarged, which matches an object between C and F.
Problem
Light moves through a medium at 2.0 × 10⁸ m s⁻¹. Find its absolute refractive index and state how it compares optically with water of index 1.33.
- 1.Use n = c/v with c = 3.0 × 10⁸ m s⁻¹.
- 2.n = 3.0 × 10⁸ / 2.0 × 10⁸ = 1.50.
- 3.Because 1.50 > 1.33, the medium is optically denser than water and carries light more slowly.
Problem
A +4 D lens and a -1.5 D lens are in contact. Find net power and effective focal length.
- 1.Add powers with signs: P = +4 - 1.5 = +2.5 D.
- 2.Use f = 1/P = 1/2.5 = +0.40 m = +40 cm.
- 3.The positive result means the combination behaves as a converging lens.
Common Confusions
| Confusion | Correction |
|---|---|
| Angles measured from the surface | Incidence and refraction angles are measured from the normal |
| Virtual means invisible | A virtual image is visible but cannot be projected because rays do not actually meet |
| All focal lengths are positive | Concave mirrors and concave lenses have negative f in the adopted convention |
| Mirror and lens formulas are interchangeable | Their distance and magnification signs differ |
| Greater mass density means greater optical density | Optical density depends on refractive index and light speed |
| Centimetres can be used directly for dioptres | Convert f to metres before applying P = 1/f |
Quiz
Which statement correctly distinguishes a real image from a virtual one?
A convex lens object is at 2F₁. Which image forms?
Which quantity has no unit?
For a mirror, u = -20 cm and v = -40 cm. What is m?
Two lenses of +3 D and -5 D are in contact. What is the combination?
Practice Problems
- A convex mirror forms an image 12 cm behind it for an object 48 cm in front. Find magnification and describe the image. Solution: u = -48 cm and v = +12 cm. m = -v/u = -(12)/(-48) = +0.25. It is virtual, erect and one-quarter the object size.
- A convex lens has f = +20 cm and u = -30 cm. Find v and m. Solution: 1/v = 1/20 - 1/30 = 1/60, so v = +60 cm. m = v/u = 60/(-30) = -2. The image is real, inverted and twice enlarged.
- Light travels from medium A at 2.4 × 10⁸ m s⁻¹ into medium B at 1.8 × 10⁸ m s⁻¹. Find nBA and predict bending. Solution: nBA = vA/vB = 2.4/1.8 = 1.33. B is optically denser, so an oblique ray bends toward the normal.
- A lens has power -4 D. Find focal length in metres and centimetres and identify the lens. Solution: f = 1/P = -0.25 m = -25 cm. The negative focal length identifies a concave lens.
- A 5 cm object forms a real lens image with magnification -1.5. Find image height and explain the signs. Solution: h′ = mh = -1.5 × 5 = -7.5 cm. The 7.5 cm magnitude shows enlargement; the negative sign shows inversion and therefore a real image in this case.
Key Takeaways
• Reflection returns light to the same medium, while refraction changes its direction across media. • Real images form by actual convergence; virtual images form by apparent convergence. • Object position relative to F and C or 2F determines image position, size and nature. • Mirror and lens formulas require different sign relationships. • Refractive index links optical density with light speed, not mass density. • Power is the reciprocal of focal length in metres and powers in contact add algebraically. • Correct units and Cartesian signs must be assigned before substitution. • A final result is trustworthy only when its signs agree with the predicted ray diagram.
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Power of a Lens
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