Refraction (AQA A Level Physics)

An optical fibre used for communications has a core of refractive index 1.65 which is surrounded by cladding of refractive index 1.55.

Figure 1

Figure 1 shows a light ray P inside the core of the fibre. The light ray strikes the core cladding boundary at Q at an angle of incidence and angle of refraction of 55.0°. 

Calculate the critical angle of the core-cladding boundary.

Calculate the angle of incidence, .   

Explain why the light ray enters the cladding at Q and therefore why total internal reflection does not occur.          

A different optical fibre is used for the communication. The speed of monochromatic light in the core is 1.64 × 10⁸ m s^–1 and the speed in the cladding is 2.51 × 10⁸ m s^–1. 

Calculate the critical angle for this light at the interference between the core and the cladding.

Figure 1 below shows three wavefronts of light directed towards a glass block in the air. The direction of travel of these wavefronts is also shown.

Figure 1

Complete Figure 1 to show the position of these three wavefronts after refraction at the surface of the glass block.

Figure 2 shows a liquid droplet placed on the glass block. A ray of light from air, incident normally on to the droplet, continues in a straight line and is refracted at the liquid to glass boundary as shown. 

Figure 2

The refractive index of the glass is 1.37. 

Calculate the fraction of the speed of the light ray in the glass block to the speed of light in a vacuum.

The speed of light in the liquid droplet is equal to 2.35 × 10⁸ m s^-1. 

Calculate the refractive index of the liquid droplet.

Calculate the angle of refraction of the light ray when it enters the glass block.

Figure 1 below shows a ray of light passing from air into glass at the top face of glass block A and into another glass block B. 

Figure 1

The refractive index of block A is 1.55 and the speed of light in block B is 2.27 × 10⁸ m s^-1. 

Show that the refractive index of block B is 1.32.

Calculate the value of  and .

On Figure 1, draw the path of the ray between block B and air.

Explain qualitatively how the angle of incidence at the block A–block B boundary should change in order for the light ray not to travel into block B at all.

Figure 1 shows a cross-section through a step-index optical fibre.

Beam A is incident at the end of the optical fibre at an angle of 13.8° to the normal and refracts into the core at 7.54° to the normal. 

Calculate the refractive index of the core.

Beam A travels through the air-core boundary and experiences total internal reflection. 

On the diagram, show the path of this ray down the fibre. Label the angle of reflection.

Beam B is incident on the end of the fibre, refracts through the air-core boundary and then refracts again when it hits the core-cladding boundary at an angle of 52.3°, travelling along the boundary.

Calculate the refractive index of the cladding.

A different step-index optical fibre is built with the same core as that in Figure 1 but replacing the cladding. 

The speed of light in the new cladding material is 1.54 × 10⁸ m s^–1. 

Explain why this new cladding material would not be suitable for sending signals through the step-index optical fibre. 

Use a calculation to support your answer.

A regular glass fish tank containing water is shown in Figure 1. Three light rays A, B and C emerge from the same point on a small object O at the bottom of the tank as shown.

Figure 1

The critical angle of the water at the water-air boundary is equal to the direction of light ray B emitted from object O from the side of the glass tank. 

On Figure 1 draw the continuation of the paths taken by the three rays shown. No further calculations are required.

The speed of the light rays in the water is 72 % of the speed of light in vacuum. 

Calculate the refractive index of the water.

Calculate the maximum angle of incidence the light rays can have at the surface of the water before total internal reflection.

The refractive index of the glass the tank is made from is 1.50.

State which of the light rays A, B or C hits the glass and explain whether or not the ray undergoes total internal reflection at the water-glass surface.

A ray of light passes from air into a glass prism as shown in Figure 1.

Figure 1

As the light ray passes through the prism, it emerges back into the air.

Calculate the critical angle from the glass to the air.

Figure 2 now shows the prism rotated and one side is coated with a film of transparent gel. A ray of light strikes the prism, at an angle of incidence of 38°, and continues through the glass to strike the glass–gel boundary at the critical angle.

Figure 2

Calculate the refractive index of the gel.

A ray of light now strikes the prism at an angle of incidence which means that it now refracts straight through the gel at the glass–gel boundary. 

Without calculation, explain how the critical angle for the glass–gel boundary differs from the critical angle for the gel–air boundary.

Diamond has certain properties which makes it one of the most sought-after gem stones for jewellery. 

Its refractive index is around 2.4, and jewellers cut it in specific ways to maximise its appeal. 

Discuss, referring to an equation, why the refractive index of diamond makes it a popular gem stone for jewellery.

Figure 1 below shows two rays of light A and B travelling through a straight optical fibre.

The overall length of the optical fibre is 0.70 km. Ray A travels down the centre of the core of the optical fibre. The path of ray B has an overall length of 0.86 km as it travels through the core. 

The refractive index of the core is 1.6 and ray A and ray B enter the fibre at the same instant. 

Compare, with a calculation, the differences between the two rays as they exit the core of the optical fibre.

Ray B is blue light that enters the core of the optical fibre at an angle of 20º as shown in Figure 2 and hits the cladding at an angle of incidence of 1º more than the critical angle.

Show that the refractive index of the cladding is 1.55.

Figure 1 shows two prisms, prism 1 and prism 2, made from transparent material and placed firmly together. A ray of light in air is incident normally on prism 1. 

Figure 1

Prism 1 is made from a denser material than prism 2 and the angle incident upon the boundary between them is below the critical angle. 

Sketch, without calculation, the path followed by the refracted ray as it enters prism 1 and prism 2 and then emerges into the air.

The refractive index of prism 1 is 1.48 and the refractive index for prism 2 is 1.20.

Calculate and label the angles of incidence and refraction on Figure 1 between:           

   (i) The prism 1 and prism 2 boundary

   (ii) The prism 2 and air boundary

Figure 2 shows the same two prisms. However, the light ray enters prism 1 at an angle of 76º to the normal.

Figure 2

On Figure 2, draw the continuation of the path of the light ray until it emerges back   into the air. Write the values of the angles between the ray and any normals you have drawn.

A different right–angled prism is in contact with a transparent substance on one of the faces as shown in Figure 3. One of the other angles in the prism is θ.

Figure 3

Refractive index of glass prism = 1.65

Refractive index of transparent substance = 1.10 

The ray enters perpendicularly to one face of the prism. It is refracted at the interface between the glass and the transparent substance. The ray eventually leaves the transparent substance at an angle of 8º to the surface of the transparent substance. 

Determine the angle θ.

Figure 1 shows a cross–section through an optical fibre used in an endoscope. The critical angle is a 7% decrease from the 75º angle to the normal at the core–cladding boundary. The refractive index of the cladding is 1.4. 

Figure `

Calculate the angle of incidence  at the air–core boundary.

Figure 2

Complete the graph shown in Figure 2 to show how the refractive index changes with radial distance along the line ABCD in Figure 1.