Refraction and Total Internal Reflection

Q1.

(a) Tick the appropriate boxes in the table below to indicate how the wavelength, frequency and speed of light are affected when a ray of light travels from air into glass.

	wavelength	frequency	speed
increase
stay the same
decrease

if frequency is correct

if both wavelength and speed are correct

[2 marks]

(b) The diagram belowshows a right-angled glass prism in contact with a transparent substance on one of the faces. One of the other angles of the prism is θ.

(i) Ray A enters perpendicularly to one face of the prism.

It is partially refracted and partially reflected at the interface between the glass and the transparent substance.

The angle of refraction is 65.0º. The ray eventually leaves at an angle α to the surface of the transparent substance.

Determine the angle α.

Let substance 1 be air,substance 2 be the transparent substance and substance 3 be glass.

The angle of incidence on the border between the substance and air = 65^o - see diagram. Always use the diagrams to mark on values....

n₁ = 1.0

n₂ = 1.09

n₁ sin θ₁ = n₂ sin θ₂

1.0 x sin θ₁ = 1.09 x sin 65^o

sin θ₁ = 0.9879

θ₁ = 81.07^o

∴ α = 9.03^o

[2 marks]

(ii) Determine the angle θ

At the glass/transparent substance boundary, the angle of refraction into the substance is 65^o.

n₃ = 1.70

n₂ = 1.09

θ₂ = 65^o

θ₃ = ?

n₃ sin θ₃ = n₂ sin θ₂

sin θ₃ = 1.09 x sin 65^o/1.70

sin θ₃ = 0.5811

θ₃= 35.5^o

∴θ = 54.5^o

[2 marks]

(c) This new diagram shows another ray entering the prism:

(i) Identify the effect that takes place at X

Total internal reflection

The word 'total' is vital for the mark to be awrded - partial internal reflection occurs whenever refraction takes place, but if the angle of incidence on the dense/rare boundary is greater than the critical angle only internal reflection occurs and it is then total internal reflection.

[1 mark]

(ii) Explain, with a diagram, how the effect that occurs at X is used to transmit information along an optic fibre.

A fibre optic cable comprises of a core surrounded by cladding of a lower optical density; therefore having a lower refractive index than the core. When a light ray enters the cable it hits the boundary between the two optical substances at an angle greater than the critical angle.

As the boundary is a dense to rare optical density boundary, the ray suffers total internal reflection.

This is repeated at each incidence point along the cable and results in the light ray being transmitted along the cable with very little loss of energy.

[3 marks]

(Total 10 marks)