Total Internal Reflection (Edexcel IGCSE Physics (Modular))

If asked to name the phenomena make sure you give the whole name – total internal reflection.

Remember: total internal reflection occurs when going from a denser material to a less dense material and ALL of the light is reflected.

If asked to give an example of a use of total internal reflection, first state the name of the object that causes the reflection (e.g. a right-angled prism) and then name the device in which it is used (e.g. a periscope)

A glass cube is held in contact with a liquid and a light ray is directed at a vertical face of the cube. The angle of incidence at the vertical face is 39° and the angle of refraction is 25° as shown in the diagram.

The light ray is totally internally reflected for the first time at X.

Complete the diagram to show the path of the ray beyond X to the air and calculate the critical angle for the glass-liquid boundary.

Answer:

Step 1: Draw the reflected angle at the glass-liquid boundary

• When a light ray is reflected, the angle of incidence = angle of reflection

• Therefore, the angle of incidence (or reflection) is 90° – 25° = 65°

Step 2: Draw the refracted angle at the glass-air boundary

• At the glass-air boundary, the light ray refracts away from the normal

• Due to the reflection, the light rays are symmetrical to the other side

Step 3: Calculate the critical angle

• The question states the ray is “totally internally reflected for the first time” meaning that this is the lowest angle at which TIR occurs

• Therefore, 65° is the critical angle

If you are asked to explain what is meant by the critical angle in an exam, you can be sure to gain full marks by drawing and labelling the same diagram above (showing the three semi-circular blocks).

Opals and diamonds are transparent stones used in jewellery. Jewellers shape the stones so that light is reflected inside. Compare the critical angles of opal and diamond and explain which stone would appear to sparkle more.

The refractive index of opal is about 1.5

The refractive index of diamond is about 2.4

 Answer:

Step 1: List the known quantities

• Refractive index of opal, n_o = 1.5

• Refractive index of diamond, n_d = 2.4

Step 2: Write out the equation relating critical angle and refractive index

Step 3: Calculate the critical angle of opal (c_o)

Step 4: Calculate the critical angle of diamond (c_d)

Step 5: Compare the two values and write a conclusion

• Total internal reflection occurs when the angle of incidence of light is larger than the critical angle (i>c)

• In opal, total internal reflection will occur for angles of incidence between 42° and 90°

• The critical angle of diamond is lower than the critical angle of opal (c_o>c_d)

• This means light rays will be totally internally reflected in diamond over a larger range of angles (25° to 90°)

• Therefore, more total internal reflection will occur in diamond hence it will appear to sparkle more than the opal

When calculating the value of the critical angle using the above equation:

• First use the refractive index, n, to find sin(c)

• Then use the inverse sin function (sin^–1) to find the value of c