Measure the angle of incidence from the normal before comparing it with the critical angle. If a diagram gives the angle between the ray and the surface, subtract that angle from 90°. Using the marked angle directly can lead to the opposite prediction.
The 2027 SEC G3 Physics K323 light topic includes the critical angle and total internal reflection. This example compares two rays at a glass–air boundary, including the case where the refracted ray travels along the boundary.
- Mark the normal at the point where the ray meets the boundary.
- Convert an angle marked from the surface.
- Check that light travels from higher to lower refractive index.
- Compare the incidence angle with the critical angle.
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Locate the two reference lines
The surface is the boundary between the materials. The normal is perpendicular to the boundary at the point where the incoming ray strikes it. The two angles between the ray and those reference lines add to 90°.
If light travels from a medium of higher refractive index to a medium of lower refractive index, the refracted ray bends away from the normal when the incidence angle is below the critical angle. At the critical angle the angle of refraction is 90° from the normal.
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Worked example | A ray 35° to the glass surface
Assume the critical angle for this glass–air boundary is 42°. A ray inside the glass strikes the boundary at 35° to the surface. The incidence angle is 90° − 35° = 55°. The ray moves from glass into the boundary with air, and 55° exceeds 42°. Total internal reflection occurs. The reflected ray makes 55° with the normal on the other side of the normal.
Try a ray 55° to the same surface. Its incidence angle is 35°, below the critical angle. A refracted ray enters the air. Some light can also be reflected inside the glass.
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Find the boundary case
At this interface an incidence angle of 42° corresponds to 48° measured from the surface. The refracted ray then runs along the boundary. For a surface angle smaller than 48°, the incidence angle is larger than 42° and total internal reflection occurs.
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Frequently asked questions
What if the light approaches from the air?
Total internal reflection cannot occur for light travelling from air towards this glass. That direction goes from lower to higher refractive index.
How can a parent check the sketch?
Ask the student to draw the normal first and label which line the marked angle touches. Have them point to the angle they will compare with 42°.