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Reflection investigation

Key idea: Trace incident and reflected rays with aligned pins, then measure both angles from the normal. Repeat at several incident angles to test whether the angles are equal.

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  • SEC G3 Combined Science Physics component 2027
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You cannot see a ray of light on paper, but you can mark it: two pins that line up when you look along them lie on the same ray. With four optical pins and a plane mirror you can trace an incident ray and its reflection, measure both angles and test the law of reflection. Optical pins are sharp, so handle them carefully.

Trace rays with pins

Most light practicals use the same technique. Two pins mark one ray.

  • Push each pin in upright, so that you can line up their bases rather than their heads.
  • Put the two pins on each ray at least 5 cm apart. A small sideways error in placing a pin then changes the direction of the line only slightly.
  • Look along the line of pins at table level with one eye closed, and move your head until the pins, or their images, appear exactly one behind the other.
  • Join the pin holes with a sharp pencil and a ruler.
  • Draw the normal at the point where the ray meets the surface: a line at 90° to the surface, drawn with a protractor or set square.
  • Measure every angle from the normal, not from the surface.
Tracing reflection with four optical pinsTop view of a plane mirror on its marked line. Two upright incident-side pins P1 and P2 define a line arriving at point P. Two observer-side pins Q1 and Q2 are aligned with the reflected images of the first two pins. Their line leaves P on the same side of the mirror. The dashed normal is perpendicular to the mirror at P. The two ray lines make equal angles with the normal. The pin pairs are spread apart; the drawing is schematic.Four pins define two ray linesincident-side pinsobserver-side pinsnormalP₁P₂Q₁Q₂irPreflecting surfacei and r are measured from the same normal at P.
Tracing reflection with four optical pinsTop view of a plane mirror on its marked line. Two upright incident-side pins P1 and P2 define a line arriving at point P. Two observer-side pins Q1 and Q2 are aligned with the reflected images of the first two pins. Their line leaves P on the same side of the mirror. The dashed normal is perpendicular to the mirror at P. The two ray lines make equal angles with the normal. The pin pairs are spread apart; the drawing is schematic.Four pins define two ray linesincident-side pinsobserver-side pinsnormalP₁P₂Q₁Q₂irPreflecting surfacei and r are measured from the same normal at P.
Align Q₁ and Q₂ with P₁ and P₂’s images; join the pin holes to trace reflection. Measure i and r from the normal.

Test the law of reflection

  1. Draw a straight line on paper on a pin board and stand a plane mirror with its reflecting surface on the line.
  2. Draw a normal to the line and an incident ray at a chosen angle i to it. Put two pins on the incident ray.
  3. Look at the images of the two pins in the mirror. Put two more pins in line with those images. They mark the reflected ray.
  4. Remove the mirror, draw the reflected ray and measure the angle of reflection r from the normal.
  5. Repeat for six angles of incidence.

Illustrative readings, recorded to the nearest degree:

i / °r / °
2021
3030
4039
5051
6060
7069

Worked example 1

Do the results support i = r?

Problem

Use the table to decide whether the results support the law of reflection.

Show full solution

  1. Look at the differences

    Method

    Find r - i for each row.

    Reason

    If i = r, every difference should be zero apart from measurement error.

    Working

    Answer

    The differences are +1°, 0°, −1°, +1°, 0° and −1°.

  2. Compare with the method's precision

    Method

    The protractor has 1° divisions; locating pins and drawing lines also contribute uncertainty.

    Reason

    Small differences of either sign can arise from measurement uncertainty. Compare the whole set rather than judging the law from one row.

    Working

    Answer

    The differences range from −1° to +1° with no consistent offset. These readings support i = r within the precision of this setup. Pin placement and pencil-line thickness affect precision as well as the protractor divisions.

  3. State the conclusion

    Working

    Answer

    The readings support i = r within the precision of this setup: all six differences lie between −1° and +1°, with no consistent offset. Small differences are expected when measuring angles.

Check your understanding 1 A steady 3° difference

For incident angles 20°, 40° and 60°, A records reflected angles 21°, 39° and 60°; B records 23°, 43° and 63°. Calculate each r-i. Which set suggests a common offset? Would averaging more readings with the same setup remove it?

Unit: °
Unit: °
Unit: °
Unit: °
Unit: °
Unit: °
Which set suggests a common offset?
Would averaging more readings with the same setup remove the offset?
Show answer

A: +1°, −1°, 0°. B: +3°, +3°, +3°. B has a systematic offset; repeating the unchanged method retains it. Check the mirror line, perpendicular normal and protractor position before repeating.

Evaluate the ray-tracing methods

SourceEffectImprovement
Pins on one ray placed close togetherA small sideways error changes the ray’s direction a lotPut the two pins on each ray at least 5 cm apart.
Lining up the heads of pins that leanThe ray is drawn in the wrong directionPush the pins in upright and line up their bases.
Block or mirror moved while placing pinsThe drawn outline no longer matches the surface the light usedHold it in place with a small weight or Blu-Tack, and redraw the outline if it moves.
Normal not at 90° to the surfaceEvery angle is measured from the wrong lineDraw the normal with a protractor or set square.
Thick pencil linesAngles can only be read to a few degreesUse a sharp pencil.

The same pin technique locates images in the mirror and lens image investigations and traces rays through glass in the refraction investigation.

Check your understanding 2 Draw rays using a shared angle reference

A pin trace has an incident ray at 30° to the mirror surface and a reflected ray at 60° to the normal. Find the incident angle from the normal and the difference r-i. Do the angles agree?

Unit: °
Show the steps Optional working
Unit: °
Unit: °
Do the angles agree?
Show answer

The incident angle is 90° − 30° = 60°. Thus r-i = 0° and the angles agree. The claimed discrepancy used different reference lines.

Check your understanding 3 Draw the pin trace

Draw the mirror, normal and both rays on paper for the trace above. Label the angles and add arrows. Compare your drawing with the model criteria below.

Show answer

Your normal is perpendicular to the reflecting surface at the ray’s meeting point. Both rays lie on the reflecting side of the mirror, on opposite sides of the normal, each at 60° to it. The incident arrow points towards the mirror; the reflected arrow points away. Use a protractor centred at the meeting point.

Common mistakes

  • Measuring angles from the mirror instead of from the normal.
  • Placing the two pins on a ray close together, so a small error changes the ray’s direction a lot.
  • Lining up the heads of leaning pins instead of their bases.
  • Letting the mirror move while placing the pins.
  • Concluding from one row instead of comparing the differences across all the readings.

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