Refraction & Total Internal Reflection

The question behind the experiment

A ray can bend at a boundary because light travels at different speeds in the two materials. This investigation turns observed ray directions into evidence about refractive index. Draw the normal to the boundary before measuring angles. Angles measured from the surface cannot be inserted unchanged into the usual Snell relationship. Record the incident medium and transmitted medium together, because the same pair of materials behaves differently when the direction of travel is reversed through the boundary.

Plan a useful comparison

Change the incident angle while keeping the materials and light wavelength fixed. Measure the refracted angle from the normal and compare the pair across several trials. A graph of the two angles is not generally a straight line, but a graph involving their sines can reveal the index relationship. State which sine is on each axis before interpreting the slope. Reversing the axes changes what the slope represents even though the underlying set of measurements remains the same.

Connect the observation to the model

Connect refractive index to light speed and wavelength. Entering a higher-index medium reduces the speed and shortens the wavelength, while the frequency remains unchanged. Along the normal, the ray can cross without changing direction even though its speed changes. Use that case to separate refraction as a material-speed effect from visible bending. A straight transmitted ray does not establish identical optical properties on both sides of the interface or an unchanged wavelength inside the material.

Interpret the result carefully

Investigate total internal reflection by sending light from a higher-index material toward a lower-index material. As the incident angle increases, the transmitted direction approaches the boundary. The critical angle marks the limiting geometry; beyond it, the ideal comparison has no propagating transmitted ray into the other medium. Partial reflection occurs before that threshold as well. Do not interpret the first visible reflection as evidence that the critical angle has already been reached in your measurement.

Build an explanation from your evidence

Use the material references to check a matched wavelength and direction. An angle read from a finite-resolution instrument cannot justify all the digits in an exact model value. Compare the observed transition with neighboring angle settings and retain that interval in your interpretation. Explain which conditions support total internal reflection and which prevent it. A high index by itself is insufficient if light is entering that material from a lower-index side rather than leaving it for the lower-index medium.

A reference case from this course

For water at the course's 650 nm reference wavelength, the critical angle toward air is 48.67012341°. The exact model value lies between instrument settings, so a practical threshold estimate should retain the angular resolution. This reference does not apply unchanged to a different wavelength or a different pair of media.

Keep the investigation reproducible

Before changing the setup, write a prediction that names the measured quantity and the expected direction of change. Retain the original trial as a reference. Record the apparatus conditions, units, and whether you used Ideal or Real lab mode. If the selected activity includes seeded variation, keep the seed and run identity with the result so another comparison does not silently mix different conditions.

Separate the observation from its explanation. A reading or a counted object belongs in the evidence; the relationship you use to interpret it belongs in the reasoning. When a result differs from the reference case, check the settings and measurement procedure before deciding that the model relationship has failed. Describe a specific source of uncertainty and where it enters your calculation. Finish with a claim supported by the recorded comparison, and identify an additional trial that could distinguish your explanation from an alternative.

Continue the comparison

Compare geometric image formation in Lenses & Mirrors and wave behavior in Double Slits & Gratings. Keep the ray model and the wave model attached to the question each investigation is designed to answer.