Physics notes, chapter 6
Light and Optics
Textbook Physics Form 4 KSSM (DLP), pages 230–282
What this chapter covers
- Explain refraction of light and use refractive index, n = c/v, and Snell's law (6.1.1–6.1.4)
- Relate real depth and apparent depth to refractive index (6.1.5–6.1.6)
- Solve problems involving refraction of light (6.1.7)
- Explain total internal reflection and the critical angle, n = 1/sin c (6.2.1–6.2.2)
- Describe natural phenomena and applications of total internal reflection (6.2.3–6.2.4)
- Describe convex and concave lenses, draw ray diagrams and state image characteristics (6.3.1–6.3.3)
- Calculate linear magnification, m = hi/ho = v/u (6.3.4)
- Use the thin lens formula 1/f = 1/u + 1/v (6.4.1–6.4.2)
- Describe the compound microscope, telescope and small lenses in cameras (6.5.1–6.5.3)
- Describe image formation by concave and convex mirrors and their uses (6.6.1–6.6.2)
6.1Refraction of light
Refraction is the change in direction of light when it travels from one medium to another of different optical density, because the speed of light changes.
Optical density is not the same as density (mass per unit volume). Oil is less dense than water, so it floats, but it is optically denser than water.
| Light travels from | Speed | Bends | Angles |
|---|---|---|---|
| Less dense to denser medium (air to glass) | Decreases | Towards the normal | i > r |
| Denser to less dense medium (glass to air) | Increases | Away from the normal | i < r |
Refractive index and Snell's law
Refractive index, n = speed of light in vacuum ÷ speed of light in the medium = c / v, where c = 3.0 × 108 m s−1. It has no unit and is always 1 or more.
| Medium | Refractive index | Medium | Refractive index |
|---|---|---|---|
| Vacuum / air | 1.00 | Perspex | 1.50 |
| Olive oil | 1.46 | Diamond | 2.42 |
Snell's law: n1 sin θ1 = n2 sin θ2. From air (n1 = 1) this becomes n = sin i / sin r. The incident ray, refracted ray and normal lie in the same plane.
Worked example
A ray in air strikes glass (n = 1.50) at i = 40°. Find r and the speed of light in the glass.sin r = sin 40° ÷ 1.50 = 0.4285, so r = 25.4°.
v = c / n = 3.0 × 108 ÷ 1.50 = 2.0 × 108 m s−1.
Real depth and apparent depth
An object under water looks nearer to the surface than it really is, because light bends away from the normal as it leaves the water.
n = real depth ÷ apparent depth = H / h
The non-parallax method (Experiment 6.2) finds the image position accurately: a pin is moved until it stays in line with the image however the eye moves.
Worked example
A coin is at the bottom of 12.0 cm of water (n = 1.33). h = H / n = 12.0 ÷ 1.33 = 9.0 cm.In a Snell's law sum, always measure angles from the normal, not from the surface of the block.
Light passes from air into a plastic with n = 1.49 at i = 60°. Find r.
Show answerHide answer
sin r = sin 60° ÷ 1.49 = 0.581, so r = 35.5°.
6.2Total internal reflection
Critical angle, c: the angle of incidence in the optically denser medium when the angle of refraction in the less dense medium is 90°.
Total internal reflection needs both conditions: light goes from a denser to a less dense medium, and the angle of incidence is larger than the critical angle.
n = 1 / sin c. The larger the refractive index, the smaller the critical angle. Diamond: sin c = 1 ÷ 2.42, so c = 24.4°.
Natural phenomena and applications
| Phenomenon or device | How total internal reflection is involved |
|---|---|
| Rainbow | Sunlight is refracted and dispersed in a raindrop, totally reflected inside, then refracted again leaving the drop |
| Mirage | Hot air near the road is optically less dense; rays from the sky are refracted away from the normal until they are totally reflected towards the eye |
| Prism periscope | Light meets the long face at 45°, larger than the prism's critical angle (42°), so it is totally reflected twice; the image is upright and the same size |
| Optical fibre | A core of high n inside cladding of low n: light is totally reflected again and again along the core (telecommunication, endoscope) |
| Cat's eye reflector | Headlight rays are totally reflected from the back surface and return to the driver |
Worked example
Optical fibre: core n = 1.60, cladding n = 1.45. At the boundary, sin c = 1.45 ÷ 1.60 = 0.906, so c = 65.0°. Rays striking the boundary at more than 65° stay in the core.Total internal reflection cannot happen when light goes from air into glass. It only happens from the denser medium.
Find the critical angle of a prism with n = 1.49.
Show answerHide answer
sin c = 1 ÷ 1.49 = 0.671, so c = 42.2°.
6.3Image formation by lenses
| Convex lens | Concave lens | |
|---|---|---|
| Effect on parallel rays | Converges them to a real focal point | Diverges them, appearing to come from a virtual focal point |
| Focal length, f | Positive | Negative |
Key terms: optical centre O (rays pass straight through), principal axis, focal point F, object distance u, image distance v, focal length f (distance OF).
Three rays for a ray diagram (convex lens)
- A ray through the optical centre goes straight on.
- A ray parallel to the principal axis is refracted through the focal point.
- A ray through the focal point is refracted parallel to the principal axis.
| Object position (convex lens) | Image position | Characteristics |
|---|---|---|
| At infinity | v = f | Real, inverted, diminished |
| Beyond 2F (u > 2f) | f < v < 2f | Real, inverted, diminished |
| At 2F | v = 2f | Real, inverted, same size |
| Between F and 2F | v > 2f | Real, inverted, magnified |
| At F | At infinity | Virtual, upright, magnified |
| Between F and O (u < f) | v > u, same side as object | Virtual, upright, magnified (magnifying glass) |
A concave lens always forms an image that is virtual, upright and diminished, between the optical centre and the focal point (v < f).
Linear magnification, m = image height ÷ object height = hi / ho = v / u. No unit. m > 1 magnified, m = 1 same size, m < 1 diminished.
Real image: it can be caught on a screen and is always inverted. Virtual image: cannot be caught on a screen and is upright.
An object is placed 8 cm from a convex lens of f = 10 cm. State the image characteristics.
Show answerHide answer
u < f, so the image is virtual, upright and magnified, on the same side as the object.
6.4Thin lens formula
1/f = 1/u + 1/v
| Quantity | Positive (+) | Negative (−) |
|---|---|---|
| Focal length f | Convex (converging) lens | Concave (diverging) lens |
| Image distance v | Real image, opposite side to the object | Virtual image, same side as the object |
Worked example
A convex lens, f = 12 cm, object at 18 cm.1/v = 1/12 − 1/18 = 1/36, so v = +36 cm and m = 36 ÷ 18 = 2. The image is real, inverted and magnified 2 times.
Worked example
A concave lens, f = −30 cm, object 60 cm away.1/v = 1/(−30) − 1/60 = −3/60, so v = −20 cm. The image is virtual, upright and diminished, 20 cm from the lens on the object's side.
Keep the signs. For a concave lens f is negative, and a negative v means a virtual image.
A convex lens, f = 15 cm. An object is 20 cm away. Find v and m.
Show answerHide answer
1/v = 1/15 − 1/20 = 1/60, so v = 60 cm and m = 60 ÷ 20 = 3.
6.5Optical instruments
| Compound microscope | Telescope | |
|---|---|---|
| Lenses | Two convex lenses of short focal length; objective fo < eyepiece fe | Two convex lenses; objective has a long fo, eyepiece a short fe |
| Object | Between fo and 2fo of the objective, close by | Distant object (parallel rays) |
| First image I1 (objective) | Real, inverted, magnified | Real, inverted, diminished |
| Final image I2 (eyepiece, used as a magnifying glass) | Virtual, magnified, inverted, at the near point (25 cm) | Virtual, magnified, inverted, at infinity (normal adjustment) |
| Lens separation | More than fo + fe | L = fo + fe |
Telescope magnification at normal adjustment: M = fo / fe. A large-diameter objective collects more light, giving a brighter image.
Small convex lenses in smartphone cameras and CCTV form a real, diminished, inverted image on the sensor. The sensor must be at least one focal length from the lens, so the focal length limits how thin the phone can be.
Worked example
Telescope with fo = 60 cm and fe = 5 cm: M = 60 ÷ 5 = 12 and L = 60 + 5 = 65 cm.Which lens, 5 cm or 60 cm focal length, is the objective of a telescope? Why?
Show answerHide answer
The 60 cm lens. A long fo with a short fe gives a large M = fo / fe.
6.6Image formation by spherical mirrors
A concave mirror reflects from the inside of a sphere; a convex mirror reflects from the outside. Terms: pole P, centre of curvature C, radius of curvature r, focal point F. The radius is twice the focal length: r = 2f.
Rays for a ray diagram
- A ray through (or towards) C is reflected back along its own path.
- A ray parallel to the principal axis is reflected through (or as if from) F.
- A ray through (or towards) F is reflected parallel to the principal axis.
| Mirror and object position | Image |
|---|---|
| Concave: at infinity | At F; real, inverted, diminished |
| Concave: beyond C | Between F and C; real, inverted, diminished |
| Concave: at C | At C; real, inverted, same size |
| Concave: between F and C | Beyond C; real, inverted, magnified |
| Concave: at F | At infinity; virtual, upright, magnified |
| Concave: between F and P | Behind the mirror; virtual, upright, magnified |
| Convex: any position | Behind the mirror, between P and F; virtual, upright, diminished |
| Mirror | Uses |
|---|---|
| Concave | Cosmetic mirror and dental mirror (magnified upright image); reflector in car headlights |
| Convex | Blind spot mirror, vehicle rear mirror, security mirror in shops: a wide field of vision |
Why is a convex mirror used as a vehicle rear mirror?
Show answerHide answer
It gives a wider field of vision, so the driver sees more of the road behind (the image is upright but diminished).
Content and figures from the Physics Form 4 (DLP) textbook, Chapter 6, pp. 230–282, redrawn and summarised.