Reflection & Refraction

Aim

• Measure pairs of angles of incidence and refraction as light passes from air into a rectangular block, plot a graph of sin i against sin r, and use the gradient to find the refractive index of the block
• The same investigation can be carried out with other shapes: a semi-circular block lets the ray enter through the curved face along a radius so it meets the flat face along the normal, which is useful for studying refraction and total internal reflection at the flat side, while a triangular prism shows how the ray refracts towards the normal on entry and away on exit, bending the same way at both faces and spreading white light into a spectrum

Variables

• Independent variable: angle of incidence, i (degrees), set by rotating the incoming ray
• Dependent variable: angle of refraction, r (degrees), read off the paper after tracing the ray
• Control variables: the same block (same material, same shape, same orientation); the same narrow beam from the ray box; the same room lighting

Apparatus

Method

1. Lay the paper flat and draw round the outline of the rectangular block with a sharp pencil
2. At a chosen point on the long edge of the outline, use the set square to draw a dashed normal line perpendicular to that edge, extending well into the air outside the outline
3. Replace the block exactly within its outline, turn on the ray box, and angle the beam so that it meets the chosen entry point at a sensible angle (begin near i ≈ 20°)
4. With the block still in place, mark four pencil dots:
   • one along the incident beam, about 5 cm before it reaches the block
   • one where the beam enters the block
   • one where the beam exits the far side of the block
   • one along the emergent beam, about 5 cm beyond the exit point
5. Turn the ray box off, remove the block, and use a ruler to join the four dots with two straight lines: the incident ray and the emergent ray (and where they intersect the outline)
6. With the protractor, measure the angle of incidence i and the angle of refraction r (the angle the ray makes with the normal inside the block)
7. Repeat steps 3–6 for at least six more angles of incidence (sensible values are 25°, 35°, 45°, 55°, 65° and 75°), using a fresh sheet of paper or a clean part of the same sheet each time

Analysis

• For every pair, calculate sin i and sin r on the calculator
• Plot sin i (y-axis) against sin r (x-axis); draw the best straight line through the points and through the origin
• The gradient of the line equals the refractive index of the block:

gradient = sin i / sin r = n

• A reasonable result for perspex is n ≈ 1.49; for crown glass n ≈ 1.50

Sources of error and safety

• Systematic errors:
  • the normal not drawn exactly at 90° to the surface (use the set square, not the protractor)
  • the ray box positioned slightly above or below the paper, so its beam is at an angle to the surface; keep the ray box level with the paper
• Random errors:
  • the beam fades and broadens with distance, so mark each ray near to its endpoints so the dot is in the middle of the visible line
  • the protractor only reads to the nearest degree, so repeat each angle three times and average
• Safety:
  • the ray box lamp gets hot, so do not touch the front bulb or aperture
  • do not stare into the beam, even via a reflection from the block