Light

01

Reflection and plane mirrors

A ray diagram shows where light travels. At a mirror, draw a normal before measuring or calculating any angle.

A ray arrow gives the direction of light travel. In the uniform medium shown, rays are straight. The normal is a line at 90° to a surface at the point where the ray meets it; it is a construction line, not a beam of light.

Measure both angles from the normal

Incident ray

The ray arriving at the surface. Its angle to the normal is the angle of incidence, i.

Reflected ray

The ray leaving the surface on the incident side. Its angle to the normal is the angle of reflection, r.

Construct and measure a reflected ray

1. Draw the mirror's reflecting line and mark the incidence point.
2. Draw a normal through that point, perpendicular to the mirror.
3. Measure i between the arriving ray and the normal. On the other side of the normal, mark the same angle.
4. Draw the reflected ray through that mark and add an arrow pointing away from the mirror.

To investigate the law, place a mirror on its traced reflecting line and direct a narrow ray at it. Mark two well-separated points along each visible ray, remove the apparatus, and join the marks with a ruler. Centre the protractor at the incidence point and use its correct scale to measure from the normal. Compare i and r for several different incident directions.

A broad beam or two marks close together makes the ray direction uncertain. A wrongly drawn normal changes the measured angles systematically; repeating the measurement does not repair that normal. Choose a protractor with suitable degree divisions and record angles to a precision the ray width and markings support.

Why a plane-mirror image appears behind the mirror

Light from one object point reflects from the mirror into the observer's eye. The reflected rays diverge, but their straight backward extensions meet at an apparent point behind the mirror. The eye receives actual reflected light; no light has to travel to that apparent point behind the mirror.

A plane-mirror image is virtual, upright and the same size as the object. It is as far behind the reflecting plane as the object is in front. It cannot be formed on a screen at its apparent position because actual rays do not converge there.

The reversed appearance of an asymmetric letter is called lateral inversion. The mirror places corresponding image points on the opposite side of its reflecting plane; it does not physically exchange two objects on your left and right.

Locate a virtual image experimentally

Trace the reflecting plane and use two sighting directions to locate an image point by backward construction. Alternatively, use a comparison marker behind the mirror with its tip visible alongside the image. Move the marker until a small sideways movement of your eye produces no relative shift between the tip and image.

This no-parallax match means that the marker tip and apparent image point are at the same position along the viewing direction. Measure their distance from the reflecting plane and compare with the object distance. Use a ruler long enough for the separation, read its millimetre divisions carefully, and measure to the reflecting plane rather than a holder or frame.

Virtual does not mean invisible. You can see the image when reflected light enters your eye. The distinction concerns where actual rays meet, not whether the image can be seen.

02

Refraction and refractive index

When light crosses a boundary between media, its speed can change. At oblique incidence, the transmitted ray then changes direction.

Draw the normal at the particular point where the ray crosses the surface. The angle of incidence i is between the arriving ray and this normal; the angle of refraction r is between the transmitted ray and the normal in the new medium.

Connect refractive index to speed

For the same light, a higher refractive index means a lower speed. It does not mean the material must have a greater mass density. When light enters a higher-index medium obliquely, it bends towards the normal. Entering a lower-index medium bends it away from the normal.

Use the sines of the angles

For a fixed pair of media and the same light, sin i / sin r is constant, with the direction of travel specified. If the first medium has index n₁ and the second has index n₂, the constant is n₂/n₁.

Follow both faces of a block

For a parallel-sided block with air on both sides, the emergent ray is parallel to the incident ray. Its sideways displacement remains: being parallel does not mean following the same line. Each face has its own normal at the crossing point.

At normal incidence, the ray travels along the normal. Its speed changes but its direction does not. Substituting i = r = 0 into the sine ratio would give 0/0, so this case cannot determine the index from that ratio.

Measure refraction through a glass block

1. Trace the block on paper and keep it on that outline. Direct a narrow ray obliquely at one face.
2. Mark entry and exit points, plus well-separated points along the incident and emergent rays.
3. Remove the block. Join entry to exit to draw the internal ray, and draw each external ray from its marks.
4. Construct a normal at the entry point and use a protractor centred there to measure i and r from the normal.
5. Repeat for several nonzero incident angles. Calculate sin i / sin r and compare the values.

A pin-tracing method can also recover the path: align separated upright pins with their viewed images through the block so they lie along the same sight line, without relative parallax. Keep the block fixed while tracing that path.

Measuring from the surface, shifting the block or using marks too close together changes the inferred angles. A thin ray, a careful outline and a longer marked baseline address different sources of uncertainty. Choose a suitable protractor scale and read it at the correct centre.

For an air-to-material investigation, a graph with sin i vertically and sin r horizontally should be approximately a straight line through the origin, with gradient n. A small scatter in measured ratios is expected; do not present the calculated table above as experimental observations.

Label the first and second media before substituting. The air-to-material shortcut cannot be used unchanged for a ray leaving the material.

03

Converging action and focal length

A thin converging lens brings a beam parallel to its principal axis to a principal focus. Focal length is the distance from the lens's optical centre to that focus.

A beam contains many rays. Here the lens is thin, surrounded by air, and used with rays close enough to its principal axis for the simple lens model.

Identify the axis, centre and focus

Principal axis

The straight reference line through the centre of the lens and its principal foci.

Optical centre

The point at the centre of the thin lens through which a ray passes essentially undeviated in this model.

Principal focus F

The point where rays initially parallel to the principal axis meet after passing through a converging lens.

Focal length f

The distance from the optical centre to the principal focus. It is a length, measured in units such as cm or m.

Light arriving from the opposite direction has a corresponding focus on the other side. Mark f on each side when using a ray diagram.

Light from a nearby object point usually arrives as a diverging bundle, rather than a parallel beam. The lens changes that bundle's direction, but its image need not be at the principal focus. The image position depends on the incoming rays.

Estimate focal length with a distant object

1. Choose a clear, sufficiently distant illuminated object. Rays from each small part of it reach the lens approximately parallel.
2. Align the lens and a screen. Move the screen to find the sharpest image.
3. Measure from the optical centre of the lens to the screen using a suitable ruler or optical-bench scale.
4. Move the screen slightly to either side of best focus to judge the uncertainty in that position.

Choose a scale covering the full separation with divisions fine enough for the focusing uncertainty. Read the lens centre's position rather than an edge of its holder, and keep lens and screen properly aligned. A finite target distance makes the incident beam only approximately parallel; using a nearer target gives an image distance that should not simply be labelled f.

F is defined using a parallel incident beam. A converging lens does not send every incoming ray to F, regardless of where that ray came from.

04

Real and virtual lens images

To classify an image, follow the rays first. Then compare the image's orientation and height with the object's.

A thin converging lens brings an axis-parallel beam to F. Rays from a nearby object point need not arrive parallel, so their meeting point can be elsewhere.

Actual convergence or apparent convergence?

Real image

Actual refracted rays from an object point meet at the image point. A screen placed there can show a sharp image.

Virtual image

The emergent rays diverge, but their backward extensions meet at an apparent image point. A screen at that apparent position cannot collect actual converging rays to form the image.

Upright or inverted

Compare orientation with the object. For the upright arrow examples, an image arrow below the axis is inverted; one above it is upright.

Magnified, same size or diminished

Compare image height with object height. A greater, equal or smaller height gives the corresponding description.

You can see both real and virtual images when the appropriate light enters your eye. A screen test concerns actual convergence, not visibility.

Read three completed diagrams

Each model uses a lens of focal length 8.0 cm and an upright object 2.0 cm tall. Identify which lines meet, then compare the image and object arrows.

First diagram: real, inverted and magnified

The actual rays meet 24 cm on the far side of the lens, 4 cm below the axis. The image is inverted and twice the 2 cm object height.

Second diagram: real, inverted and diminished

The rays meet 12 cm on the far side, 1 cm below the axis. The image is inverted and half the object height.

Third diagram: virtual, upright and magnified

Backward extensions meet 8 cm on the object's side, 4 cm above the axis. The actual emergent rays diverge. The image is upright and twice the object height.

These descriptions come from the completed ray paths and labelled sizes. The same converging lens can produce different image characteristics; it does not always magnify.

Find an image and describe what you observe

For a real-image investigation, align an illuminated arrow, the lens and a screen along the principal axis. Move the screen until the image is sharp. Measure the image distance from the lens centre, then compare image height and orientation with the object. Use the same length units for a size comparison.

Move the object to another suitable position and refocus the screen. Keep the alignment and distinguish the lens-to-object distance from the lens-to-screen distance. A millimetre ruler can measure positions and heights, but a blurred edge limits how precisely the image height can be read.

For a supplied arrangement known to produce a virtual image, look through the lens at the object and describe the apparent image. It can be seen even though a screen at the apparent position does not show it. Its image position may be inferred from backward ray extensions.

A blurred screen is not proof of a virtual image. The screen may simply be in the wrong place or the apparatus misaligned. Use the ray behaviour and the stated setup as evidence.