A ray of light changes direction when it enters a transparent material at an angle because its speed changes. In a rectangular glass block, that change can be investigated with a ray box, pencil lines, a ruler and a protractor. The essential examination skill is to measure each angle from the normal, not from the glass surface, then explain what the emerging ray reveals.
This G3 SEC Physics learner’s guide develops refraction from the simplest ray diagram to a trustworthy practical investigation. It follows the earlier lessons on mirrors, real images and magnifiers, but takes ownership of a different problem: how to trace and measure light passing through a boundary. Every numerical example here is constructed for teaching, not taken from a live examination paper.
- Core idea: light bends towards the normal when it passes from air into ordinary glass at a non-zero angle, and away from the normal when it leaves glass for air.
- Key measurements: angle of incidence, angle of refraction, the normal, and corresponding incident and emergent rays.
- Mathematical relationship: for the same two media, sin i divided by sin r is constant when the angles refer to the same interface and travel direction.
- Practical method: trace the block, mark the rays, remove the block before measuring and repeat several angles.
- Next learning routes: Mathematics will check sine ratios; English will test concise reporting; the final EMS chapter will audit the complete evidence.
What changes when a ray enters glass?
Imagine a narrow beam travelling through air towards a transparent glass block. If the ray strikes the surface straight on, it continues along the same line. It may still change speed, but its direction does not change. If the beam strikes at an angle, the transmitted ray usually bends. The bending is called refraction. It is not a second name for reflection. A small amount of light may reflect at a surface, but the refracted ray is the light that passes into the second material.
The direction matters. From air into ordinary glass, the refracted ray moves closer to the normal. From glass back into air, the ray moves farther from the normal, provided transmission takes place. Do not memorise these as decorative phrases. Draw the boundary and the normal first. Compare angles from that reference line. The path should then make visual and physical sense.
This is the next useful step after Volume 0480 on magnifiers. A lens uses refraction, but a glass block gives us a simpler boundary where we can examine the change deliberately.
The normal is the reference line, not another light ray
The normal is an imaginary straight line drawn at ninety degrees to a surface at the point where a ray arrives. On a diagram it is usually shown as a dashed line. It does not describe where light travels. Instead, it gives us a consistent reference for measuring the ray’s angle. The angle of incidence is between the incoming ray and the normal. The angle of refraction is between the transmitted ray and the normal.
A frequent error is to measure from the glass surface. Suppose the incoming ray makes thirty degrees with the surface itself. The angle of incidence is sixty degrees, not thirty. Those two numbers add to ninety degrees because the normal and the surface are perpendicular. If a question says “angle with the surface,” translate it before applying any formula.
Students sometimes draw the normal at the wrong point, especially when the block has several faces. Each interface requires a normal at the exact crossing point. Draw the entry normal at the entry face and the exit normal at the exit face. They may be parallel for a rectangular block, but they are still separate reference lines.
Read a ray diagram in a fixed order
Start with the medium through which the ray is already travelling. Label air outside the block and glass inside it. Identify the boundary that is actually being crossed. Draw the normal through the point of incidence. Mark the incident direction with an arrow, then identify which ray continues into the second medium. Finally, compare the measured angles on the correct side of the normal.
This order protects against a common visual trap. A sloping line can appear to move towards the normal when the diagram is mentally turned upside down. Rather than trusting that first impression, ask whether the measured angle becomes smaller or larger. Entering glass from air should normally give a smaller refracted angle. Leaving glass for air should normally give a larger angle, as long as a transmitted ray exists.
A complete ray diagram needs arrows. Without them, the same three straight segments could be misread as travel from right to left rather than left to right. If a question provides no arrows, read its wording carefully before assuming the travel direction.
Why a rectangular block produces a parallel emerging ray
Consider a block with two opposite parallel faces. A ray from air enters at the first face, travels through glass, and leaves through the second face. At entry, it bends towards the normal. At exit, it bends away from the normal. Because the faces are parallel and the outside medium is air on both sides, the emerging ray is parallel to the original incident ray in an ideal uniform block.
Parallel does not mean coincident. The emerging ray is generally displaced sideways from the straight-line path it would have taken if the block were absent. This sideways displacement is called lateral displacement. Its size depends on the block thickness and the entry angle. Students should be able to identify the effect on a tracing without inventing a formula that the question has not supplied.
If the faces are not parallel, such as in a prism, the emerging ray need not be parallel to the incident ray. Never carry the rectangular-block conclusion into every transparent object. The conclusion belongs to a particular geometry and arrangement of media.
Refraction is not caused by a ray choosing the shortest route
The ray does not make a decision. Light travels differently in different optical media, and a change in speed at a boundary can change the direction of propagation. For ordinary glass, the speed of light is lower than in air. This helps explain the observed bend towards the normal on entering the glass.
It is useful to separate description from explanation. “The ray bends towards the normal” tells us what the ray does in a specified case. “Its speed is different in the two media” connects the observation to the underlying physical model. A question asking for a description may be answered with a well-labelled path. A question asking why needs the change of speed as well.
Do not say that light always slows down whenever it enters any transparent medium. The comparison depends on the media and the direction of travel. The air–glass case is familiar, but the rule should be phrased in terms of relative optical properties rather than a blanket statement about every boundary.
The sine relationship and what it means
For refraction at a particular boundary, a useful relationship is sin i divided by sin r equals a constant, when i and r are correctly defined for a fixed direction between the same pair of media. The official G3 Physics syllabus names this relationship explicitly. The constant can be estimated from measurements at several non-zero angles. A stable result supports a consistent refraction model.
For a ray going from air into glass, an illustrative reading of i = 30 degrees and r = 19.5 degrees gives sin 30 degrees approximately 0.500 and sin 19.5 degrees approximately 0.334. Their ratio is about 1.50. Another reading, i = 45 degrees and r = 28.1 degrees, yields approximately 0.707 divided by 0.471, again close to 1.50. Small differences are unsurprising when measurements have limited precision.
These numbers are teaching examples. An examiner may give other angles, a different optical medium, or a graph. The method survives the change: verify which angle is which, use a calculator in degree mode, compute the ratio with sensible precision, and interpret why several values should be approximately consistent.
Refractive index connects the ray to speed
The refractive index of a medium is defined as the speed of light in vacuum divided by its speed in that medium. The ratio has no unit. A refractive index of approximately 1.50 means that light travels at about two-thirds of its vacuum speed in that simplified example. It does not mean that the speed is 1.50 times faster. A larger refractive index means a lower speed relative to the vacuum speed.
The sine ratio measured for air-to-glass refraction is close to the glass refractive index when the refractive index of air is approximated as one. Strictly, the comparison at a boundary depends on the refractive indices of both media. Keep that distinction clear when moving beyond the familiar air-and-glass context.
The examination may ask for a definition of refractive index, a speed calculation, or an explanation of how angle measurements reveal the medium’s optical behaviour. These are related but not identical tasks. State the required relationship first, then substitute the correct known values.
What happens at normal incidence?
If the incident ray travels along the normal, its angle of incidence is zero. The refracted ray also travels along the normal, so the direction is unchanged. It is incorrect to conclude from the straight line that the material did not affect the light’s speed. Direction and speed are different properties.
A particularly important mathematical caution arises here. Both sin 0 degrees and sin 0 degrees are zero. The expression zero divided by zero cannot determine the refraction constant. Therefore a normal-incidence observation is useful for checking the alignment of the apparatus, but not for calculating a sine ratio. Choose non-zero angles when estimating the constant experimentally.
A strong answer might say: “At normal incidence the ray passes straight through the boundary without changing direction, although its speed changes. The zero-angle trial does not supply a usable sine ratio.” That response explains the observation and its measurement limit without adding unsupported claims.
Set up a clean glass-block experiment
Place a sheet of paper on a stable surface. Position the rectangular glass block and trace its outline using a sharp pencil. Keep the block fixed while directing a narrow light ray at an entry face. Mark two well-separated points along the incident path and two along the emerging path. Repeat for other incidence angles while recording each trial clearly.
Remove the block before drawing the internal path. Join the entry point to the exit point through the outline, guided by the traced rays. Use a ruler to make straight construction lines, then draw normals at both faces. Measure i and r with a protractor whose centre is at the correct boundary point. It is often better to draw a large, uncluttered diagram than to squeeze every angle into a tiny corner.
Use school-approved optical equipment under the teacher’s instructions. Do not stare directly into the beam. The task is a controlled practical demonstration, not a contest to make the light source brighter. Clear lines, careful handling and reliable records are more valuable than an impressive-looking beam.
Why two marked points are better than one
One isolated mark gives a position but not a secure direction. Two separated points allow a straight line to be drawn along the ray path. If the points are too close, a small marking error can create a large angular error after the line is extended. This is a geometric reason for spacing the points sensibly, not merely a laboratory tradition.
Keep the pencil thin and the protractor aligned. A fat pencil line can make the entry point ambiguous. A protractor positioned several millimetres away from the true intersection will produce a questionable reading even if its scale is accurate. Accuracy begins with the construction, before any number is written.
When a pair of points appears inconsistent with other evidence, inspect the tracing instead of quietly moving the marks to make a prettier result. Good practical work records observations first and explains uncertainty afterwards. It does not alter measurements to fit a remembered textbook angle.
Record a table that can actually be checked
A useful table has columns for trial number, angle of incidence in degrees, angle of refraction in degrees, sin i, sin r and the sine ratio. If the question asks only for angles, do not overload the table; but when calculating a relationship, keep the raw angles alongside the derived values. That permits another person to reproduce the calculation.
For example, three illustrative air-to-glass trials might use 20 degrees and 13.2 degrees, 30 degrees and 19.5 degrees, and 45 degrees and 28.1 degrees. Their ratios are approximately 1.50, 1.50 and 1.50 after reasonable rounding. These are deliberately consistent synthetic values. Actual school measurements will show some spread because of finite line thickness, angle reading and alignment.
Put units in the heading, not after every angle in the column. Sine values and ratios are dimensionless. Record the observed angles with the precision that the measuring instrument warrants. Reporting a hand-read angle as 27.38491 degrees creates a false impression of precision.
Graph the relationship rather than guessing at a trend
A graph of sin i against sin r is a useful way to look for proportionality. If sin i is placed on the vertical axis and sin r on the horizontal axis, the gradient is approximately the constant sin i / sin r. If you reverse the axes, the gradient is the reciprocal. Neither graph is automatically wrong; the labels determine the interpretation.
Use a sensible scale and plot the measured points. When the data support a straight-line pattern, draw a best-fit line rather than joining each point into an artificial zigzag. The slope can be estimated using two well-separated points on the line, not necessarily two raw data points that are especially convenient.
A line that does not pass exactly through one plotted point is not automatically poor. Measurement data have uncertainty. What matters is whether the line reasonably represents the overall pattern. However, do not force an obviously curved or scattered relationship into a straight line without comment.
Practical errors and how to repair them
Common errors include measuring from the surface, placing the protractor centre away from the point of incidence, moving the block after tracing its outline, and drawing a normal that is not perpendicular. Another frequent problem is confusing the ray that reflects back into air with the ray that travels through glass. These errors change the physics being measured, not merely the appearance of the drawing.
A good improvement responds to a specific weakness. If a thick beam makes the ray direction uncertain, use a narrower ray or mark its centre consistently. If pencil lines are broad, use a sharper pencil. If points are close together, increase their separation where the setup allows. If alignment is unstable, secure the sheet and maintain the block position.
“Repeat the experiment” can be helpful, but it is not a complete improvement unless you say what repetition is meant to reveal. Repeating independent measurements can expose variability. It cannot automatically correct a systematically misplaced protractor or an incorrectly defined normal.
Distinguish an observation, a deduction and a claim
“An incident angle of 40 degrees produced a refracted angle of approximately 25 degrees” is an observation when it is supported by the experiment record. “The ray bends towards the normal on entering glass” is a description derived from the measured geometry. “The ratio is close to 1.50 across the trials” is a calculation-based result. “Every transparent block behaves exactly like this one” is an unjustified generalisation.
This distinction matters in G3 Physics structured answers. If asked to state what the table shows, refer to the numbers or trend. If asked to explain, link the trend to the refraction model. If asked to evaluate reliability, consider the range of observations, the measuring process and whether the conclusion exceeds the data.
The same habit prepares students for English comprehension, where a writer’s assertion is not always the same as the evidence the writer supplies. The later integrated chapter will use this separation without repeating the complete Physics explanation.
Reading the practical examination correctly
The official 2027 G3 Physics K323 assessment includes Paper 1 multiple choice, Paper 2 structured and free response, and Paper 3 practical. Paper 1 is one hour with 40 marks and a 30 per cent weighting; Paper 2 is one hour forty-five minutes with 80 marks and a 50 per cent weighting; Paper 3 is one hour fifty minutes with 40 marks and a 20 per cent weighting. These details come from the published SEAB syllabus, not from the examples on this page.
A ray diagram may appear as a short conceptual task, a numerical question, or part of an experiment that requires construction and evaluation. Prepare for the underlying skills rather than betting on a particular diagram. Learn to define terms, calculate carefully, explain a trend and identify how to improve a practical method.
A student who can recite the refraction rule but cannot place a protractor on the correct angle has not finished learning the topic. Similarly, accurate measurement without a physical explanation is only half a response.
Worked decisions: identify the correct move
Decision 1 — Surface or normal? A ray makes 35 degrees with the surface of a glass block. Since the normal is perpendicular to the surface, the angle of incidence is 55 degrees. Do not insert 35 degrees into a refraction formula merely because it is the only number printed. The phrase describing the reference line determines which angle you need.
Decision 2 — Straight path, changed speed. A ray travels along the normal from air into glass. The direction remains unchanged, but the light travels at a different speed in the glass. A diagram should show an undeviated transmitted ray, not an imaginary bend inserted simply to demonstrate that refraction has occurred at a boundary.
Decision 3 — Entering the block. An air-to-glass ray has i = 50 degrees. A candidate draws the refracted angle as 63 degrees. For ordinary glass the refracted angle should be smaller than the incident angle. Before doing arithmetic, check the geometry. The stated drawing is inconsistent with the usual direction of bending.
Decision 4 — Leaving the block. Inside the glass a ray meets the glass–air boundary with a moderate angle and emerges. Its angle in air is larger than its angle in glass. That is not a contradiction of the previous rule: it is the reverse journey. Identify the first and second media each time.
Decision 5 — Parallel faces. An emerging ray from a rectangular block is parallel to its incoming ray but appears shifted sideways. This is expected for an ideal rectangular block with air on both sides. The student should not erase the displacement in order to connect the lines. The offset is useful evidence of the ray’s changed path.
Decision 6 — A different shape. A triangular prism gives an emerging ray that is not parallel to the incident ray. The student claims the experiment must be wrong because all transparent solids make parallel emerging rays. The correction is to restrict the parallel-ray rule to appropriate parallel-face geometry.
Decision 7 — Calculator mode. To calculate sin 30 degrees, a calculator in degree mode gives 0.500. If it is mistakenly left in radian mode, its result is unsuitable for these angle measurements. A final numeric answer must be checked against the diagram as well as the button presses.
Decision 8 — The 30-degree trial. Suppose i = 30 degrees and r = 19.5 degrees. The approximate values sin i = 0.500 and sin r = 0.334 give a ratio of about 1.50. Write the ratio with no unit. It compares two sine values, not two lengths or two measured angles directly.
Decision 9 — The 45-degree trial. Suppose i = 45 degrees and r = 28.1 degrees. The ratio is approximately 0.707 / 0.471 = 1.50. If the student instead divides 45 by 28.1, the answer is about 1.60, but this is not the required sine relationship. Never replace a trigonometric rule with a raw angle ratio.
Decision 10 — Zero degrees. A zero-incidence observation has sin i = 0 and sin r = 0. It cannot be used to compute the experimental ratio because zero divided by zero is undefined. Retain the observation as an alignment check and use other angles for a numerical estimate.
Decision 11 — Missing unit. A table records i and r in degrees but labels sin i in degrees too. The sine of an angle is a dimensionless number; remove that unit from the sine column. Unit discipline is not optional decoration. It reveals whether the student understands what has been calculated.
Decision 12 — An uncertain marking. Two pencil dots on the emerging ray are only a few millimetres apart. When joined, a tiny change in one dot changes the angle noticeably. Place two clear, well-separated marks where feasible, then trace the line. Improving the geometry is more useful than averaging several bad readings.
Decision 13 — A wide beam. The ray box produces a broad illuminated strip. The student chooses a different edge of the strip on each trial. The measured angles become inconsistent. A narrower beam, or a consistent centreline rule, addresses the actual source of uncertainty.
Decision 14 — A moved block. The traced outline no longer matches the block position when the final ray is marked. The internal line reconstructed after removing the block may not represent the true path. The solution is to repeat that trial with the block held fixed, not to invent a missing entry point.
Decision 15 — Two data sets. Group A records sine ratios of 1.48, 1.51 and 1.50. Group B records 1.36, 1.63 and 1.47. The groups have similar central values, but Group A is more consistent in this small example. Do not automatically say Group A is more accurate without a trusted reference or calibration.
Decision 16 — Graph axis order. A graph places sin r on the horizontal axis and sin i on the vertical axis. A calculated gradient close to 1.50 matches sin i divided by sin r. If the axes are reversed, the gradient would be around 0.67 for the same relationship. Always state the axes before naming a gradient.
Decision 17 — Graph origin. The plotted experimental line is close to the origin but does not intersect it exactly. Inspect the scatter and measurement precision before deciding whether that small offset is meaningful. A physical relationship can be well supported without every imperfect point landing precisely on an ideal line.
Decision 18 — Speed interpretation. If a medium has refractive index 1.50, light travels in it at approximately c / 1.50. It does not travel at 1.50c. A ratio larger than one is the vacuum speed divided by the medium speed, so the direction of the division matters.
Decision 19 — Observation versus inference. A student writes, “The ray probably bent because the block is very expensive.” Price was not measured and does not explain refraction. A supported response refers to direction, angle, medium and speed, then distinguishes the recorded facts from the physical model.
Decision 20 — Improvement with purpose. A response says, “Use better equipment.” That is too vague. A more useful recommendation is to replace an overly thick pencil mark with a fine line because it reduces uncertainty in finding the exact intersection and hence the measured angle.
How to study this topic without confusing its parts
Begin with six simple diagrams showing air-to-glass entry, glass-to-air exit and normal incidence, each in two orientations. On every drawing label the medium, normal, incident ray, transmitted ray and angles. Ask another student to identify the ray direction without hearing your explanation. If they cannot, the arrows or labels are not clear enough.
Next perform numerical checks on carefully chosen pairs of non-zero angles. For each pair, estimate whether the refracted angle should be smaller before calculating a sine value. Record the calculator mode and the dimensionless ratio. Move on to practical evidence: draw a fresh rectangular block, construct the ray path and write two improvements that fix named measurement weaknesses.
Finally, explain the whole experiment in a short oral account. State what was changed, what was measured, which comparison was made, what was concluded and what limitations remain. The ability to explain a method without reading from the notes is stronger evidence of understanding than recognition of a memorised diagram.
Examination-style questions with full reasoning
Question A. A ray makes 62 degrees with a glass surface before entering the block from air. Find its angle of incidence. Answer: 28 degrees, because the normal is perpendicular to that surface. The given value describes the complement of the required angle. Write the subtraction visibly so the examiner can follow the reference change.
Question B. A candidate records i = 60 degrees and r = 35.3 degrees for an air-to-glass interface. Estimate sin i divided by sin r. Answer: sin 60 degrees is about 0.866 and sin 35.3 degrees is about 0.578, giving approximately 1.50. Keep the calculator in degree mode and report a result consistent with the data precision.
Question C. Why does a ray that enters and leaves a uniform parallel-sided glass block emerge parallel to its original direction? Answer: refraction at the first face changes the direction towards the normal, and refraction at the second, parallel face reverses that angular change as the ray returns to the original external medium. A sideways displacement can remain.
Question D. A learner uses only one marked point to construct the emergent ray. What is missing? Answer: a second point on the path, or other reliable directional evidence, is needed to establish the line. Marking two separated points reduces the angular effect of small positional uncertainty.
Question E. Three ratios are 1.49, 1.50 and 1.51. Can the learner announce that the exact refractive index of every glass block is 1.50? Answer: no. These measurements support an approximate value for the tested arrangement. Other materials may have other refractive indices, and these measurements have limited precision.
Question F. Why is it misleading to describe a straight transmitted ray at normal incidence as proof that light did not change speed? Answer: unchanged direction does not imply unchanged speed. A direction change is not necessary at zero incidence, even though the speed depends on the optical medium.
Question G. A candidate draws the normal at the centre of the block, not where the ray hits its surface. Why is the diagram defective? Answer: angles are measured at the interface crossing. A displaced normal may be parallel to the correct line but makes the construction and angle labelling ambiguous, especially when a ray path must be traced accurately.
Question H. A graph of sin i on the vertical axis against sin r on the horizontal axis has a gradient of 1.48. What does that represent? Answer: an experimental estimate of the sine ratio for the investigated boundary and direction. Check the axes before identifying it as a refraction-related constant; a reversed graph would give its reciprocal.
Know where this chapter ends
This chapter owns the physical ray path and the practical measurement method for refraction through a rectangular glass block. It does not try to replace the complete Maths treatment of sine, inverse sine and numerical error. Volume 0485 takes responsibility for those computations. The following English chapter uses source material to practise the official Paper 2 summary task, while the subsequent EMS chapter checks whether all three kinds of evidence justify an exhibition claim.
For earlier optics steps, return to Volume 0472 on reflection, Volume 0476 on real-image lens tests and Volume 0483 on integrated evidence. The Science Hub is the stable subject route; the Mathematics Hub and Secondary English Learning Hub support their own skills. Students rebuilding earlier habits can use the PSLE Learning Guide.
Official syllabus checks and final takeaway
The SEAB list of 2027 G3 syllabuses, last updated 26 October 2026, identifies Physics as K323 rather than the pre-2027 reference code 6091. The official K323 syllabus, especially its Light learning outcomes and practical guidance, is the authority for examination scope, not any invented question in this guide. The 2027 SEC will replace the earlier N- and O-Level qualifications while retaining the corresponding subject-level standards.
Make one habit permanent: draw the normal before measuring any angle. From that one decision follow a reliable diagram, the right sine ratio and an explanation that distinguishes what was seen from what was inferred. The skill seems small, but it is exactly the sort of foundation that makes more complex examination questions manageable.
