5.1.1 Reflection, refraction and total internal reflection

Reflection: angles are measured from the normal

1. A ray is a straight line with an arrow that shows the direction in which light travels.
2. The normal is an imaginary line drawn at $90^{\circ }$ to the surface at the point where the ray meets the boundary.
3. The angle of incidence, $i$, is the angle between the incident ray and the normal.
4. The angle of reflection, $r$, is the angle between the reflected ray and the normal.
5. The law of reflection is $i=r$, so the incident ray and reflected ray make equal angles with the normal.
6. A ray travelling along the normal has $i=0^{\circ }$ and is reflected back along the same path.

Refraction: speed changes at a boundary

1. When light enters a more optically dense medium, such as glass from air, it slows down and bends towards the normal.
2. When light enters a less optically dense medium, such as air from glass, it speeds up and bends away from the normal.
3. Light travelling along the normal changes speed but does not change direction because its angle of incidence is $0^{\circ }$.
4. The frequency of the light is fixed by the source and does not change at the boundary.
5. Since $v=f\lambda$, a lower speed at unchanged frequency means a shorter wavelength in the more optically dense medium.
6. At a glass boundary, part of the light can be refracted and part can be reflected.

Total internal reflection needs two conditions

1. The critical angle, $c$, is the angle of incidence in the optically denser medium that produces an angle of refraction of $90^{\circ }$.
2. At $i<c$, some light leaves the denser medium by refraction and some can be reflected.
3. At $i=c$, the refracted ray travels along the boundary because its angle to the normal is $90^{\circ }$.
4. At $i>c$, total internal reflection occurs and no refracted ray leaves the medium.
5. Total internal reflection can occur only when light travels from a more optically dense medium to a less optically dense medium, such as glass to air.
6. Optical fibres use repeated total internal reflection to guide light along the transparent core, including around gentle bends.

5.1.2 Specular and diffuse reflection

Surface roughness controls reflected-ray directions

1. A smooth surface has normals pointing in almost the same direction at neighbouring points.
2. Parallel rays therefore strike at the same angle of incidence and leave at the same angle of reflection.
3. The reflected rays remain ordered, so a clear image can form in a mirror, still water or polished metal.
4. Each ray obeys $i=r$.
5. A rough surface has microscopic slopes, so the normal points in a different direction at each point.
6. Each ray still obeys $i=r$ relative to its own local normal, but the reflected rays travel in different directions.
7. The scattered rays do not preserve the ordered pattern needed for a clear image.
8. Paper, unpolished wood and a painted wall usually produce diffuse reflection.

Diffuse reflection makes objects visible from many positions

1. A smooth surface directs most reflected light into a narrow range of directions, so glare or a bright reflected image may be seen from only certain positions.
2. A rough surface sends reflected light towards observers in many positions, which is why writing on paper can be read from different angles.
3. Diffuse reflection does not mean that light is absorbed; it means that the reflected light leaves in many directions.

5.1.3 Colour of light: absorption and filters

Object colour depends on which wavelengths reach the eye

1. White light contains the visible wavelengths that the eye interprets as different colours.
2. An opaque surface appears a particular colour because it reflects that colour or range of colours and absorbs most of the others.
3. A red object in white light reflects red light and absorbs most other visible wavelengths.
4. A white surface reflects most visible wavelengths, while a black surface absorbs most visible wavelengths.
5. The observed colour depends on both the wavelengths in the incident light and the wavelengths the surface reflects.
6. A red object illuminated only with blue light appears very dark because there is no red light to reflect and the blue light is mostly absorbed.

Filters transmit selected colours

1. A red filter transmits red light and absorbs most other visible colours.
2. A filter cannot create a missing colour; it can only transmit wavelengths already present in the incident light.
3. White light passing through a blue filter appears blue because blue wavelengths are transmitted while most other wavelengths are absorbed.
4. Red light incident on a blue filter produces little or no transmitted light because the blue filter absorbs the red light.
5. Two filters in sequence transmit only wavelengths that both filters allow through.

Use a wavelength pathway to explain colour

1. First identify the wavelengths present in the light source.
2. Then state which wavelengths the surface reflects and which it absorbs.
3. If a filter is present, state which remaining wavelengths it transmits and which it absorbs.
4. The colour reaching the eye is the wavelength that survives every stage.

5.1.4 Lenses: power, focal length and shape

Lens power increases as focal length decreases

1. The principal axis is the straight line through the optical centre and both principal foci.
2. The optical centre is the central point of a thin lens through which a ray passes without changing direction.
3. The power of a lens measures how strongly it converges or diverges light.
4. Lens power is calculated using $P=\frac{1}{f}$, where $P$ is in dioptres, $D$, and $f$ is in metres, $m$.
5. A shorter focal length gives a larger magnitude of power because the rays are bent more strongly.
6. A converging lens has positive power, while a diverging lens has negative power.

Shape determines how strongly a lens bends light

1. A more strongly curved converging lens changes the direction of rays more, so it has a shorter focal length and a larger positive power.
2. A less strongly curved converging lens bends rays less, so it has a longer focal length and a smaller positive power.
3. A more strongly curved diverging lens spreads rays more, so the magnitude of its negative power is larger and its focal length has a smaller magnitude.
4. Lens material also affects refraction, but comparisons of shape assume the same transparent material.

Power must be compared using magnitude and sign

1. The sign identifies the type of lens: positive for converging and negative for diverging.
2. The magnitude, $|P|$, identifies the strength of the lens.
3. A lens of $-6D$ is stronger than a lens of $+2D$ because $6>2$, although the lenses bend rays in opposite ways.

5.1.5 Ray diagrams for converging and diverging lenses

Ray diagrams use three predictable rays

1. Draw the lens, the principal axis, a principal focus on each side and an upright object before drawing rays.
2. Use a ruler, place arrowheads on rays and draw at least two construction rays from the top of the object.
3. The image is located where refracted rays meet, or where their backward extensions meet.

A converging lens bends parallel rays through the focus

1. A ray parallel to the principal axis is refracted through the principal focus on the far side of a converging lens.
2. A ray through the optical centre continues undeviated.
3. A ray directed through the principal focus on the near side emerges parallel to the principal axis.
4. Any two of these rays are sufficient to locate the image; the third ray checks the construction.
5. When refracted rays actually meet, draw the image at their intersection.

A diverging lens makes rays spread out

1. A ray parallel to the principal axis is refracted so that it appears to have come from the principal focus on the same side as the object.
2. Draw this refracted ray away from the axis, then extend it backwards with a dashed line through the near focus.
3. A ray through the optical centre continues undeviated.
4. The backward extensions meet on the same side as the object, between the lens and the near focus.
5. A diverging lens therefore produces a virtual, upright and diminished image for a real object.

Object position changes a converging-lens image

1. With the object beyond $2F$, the image forms between $F$ and $2F$ and is real, inverted and diminished.
2. With the object at $2F$, the image forms at $2F$ and is real, inverted and the same size.
3. With the object between $F$ and $2F$, the image forms beyond $2F$ and is real, inverted and magnified.
4. With the object at $F$, emerging rays are parallel and the image is effectively at infinity.
5. With the object between the lens and $F$, the emerging rays diverge and their backward extensions form a virtual, upright and magnified image on the object's side.

5.1.6 Real and virtual images

Real images form where light rays meet

1. A converging lens produces a real image when the object is farther from the lens than the focal length.
2. The image forms on the opposite side of the lens from the object.
3. A real image produced by a single converging lens is inverted.
4. Its size depends on object position: it can be diminished, the same size or magnified.
5. A camera sensor, cinema screen and the retina receive real images because light rays reach those surfaces.

Virtual images form where rays appear to meet

1. A converging lens produces a virtual image when the object is between the lens and its principal focus.
2. That image is upright, magnified and on the same side of the lens as the object.
3. A diverging lens produces a virtual, upright and diminished image for every position of a real object.
4. In a ray diagram, dashed backward extensions meet at the virtual image position, but no light travels along those extensions.
5. A magnifying glass works by placing the object inside the focal length of a converging lens, so the eye receives diverging rays that appear to come from a larger upright image.

Image descriptions use four properties

1. State whether the image is real or virtual.
2. State whether it is upright or inverted.
3. Compare its size with the object using magnified, same size or diminished.
4. State its position relative to the lens, object and principal focus where the diagram provides that information.
5. A screen test distinguishes image type: a sharp image on a screen is real, while an image visible only by looking into the optical system is virtual.