Pupil sheet · Refraction and total internal reflection

Total internal reflection — questions

Name ______________________ Date ____________

Try every question before you use a nudge. Write in full sentences where you are asked to explain.

1. state

Which statement gives the meaning of the critical angle?

Circle one answer.

The angle between the ray and the surface, inside the medium, when no light gets out.
The angle of incidence, in the air, at which light stops getting into the medium.
The angle of incidence, inside the medium, at which all of the light is reflected.
The angle of incidence, inside the medium, at which the angle of refraction is 90°.

Nudge (only if you are stuck): At the critical angle, where does the ray in the air go?

2. identify

Three rays of light, P, Q and R, travel inside a semicircular block of clear plastic and meet the middle of its flat side. The critical angle of the plastic is 37°. The angles of incidence at the flat side are: ray P, 61°; ray Q, 22°; ray R, 37°. Match each ray to what happens at the flat side. One option is not used.

Write the number of the matching option.

The ray in the air runs along the flat side.
No light leaves: all of it is reflected inside.
All of it leaves, and none is reflected.
Most leaves, bent away; a weak ray is reflected.

Ray P (61°): ______
Ray Q (22°): ______
Ray R (37°): ______

Nudge (only if you are stuck): What happens at the critical angle itself? Start from that ray, then think of a ray on each side of it.

3. explain

Leon shines a torch from the air onto the water surface in a fish tank at a large angle of incidence, 80°. He expects all the light to be totally internally reflected. Is Leon right? Which statement is correct?

Circle one answer.

No: at 80°, the ray in the water runs along the surface, at 90° to the normal.
No: going from air into water, light bends towards the normal and always gets in.
Yes: at 80°, light slows down so much at the surface that it cannot get in.
Yes: 80° is bigger than the critical angle of water, so all of the light is reflected.

Nudge (only if you are stuck): In which direction is the light crossing the surface: into the water, or out of it?

4. identify

Which row gives both of the conditions needed for total internal reflection?

Row	Where the light is	Angle of incidence at the boundary
A	in the faster medium, meeting a slower one	bigger than the critical angle
B	in the slower medium, meeting a faster one	equal to the critical angle
C	in the slower medium, meeting a faster one	bigger than the critical angle
D	in the slower medium, meeting a faster one	smaller than the critical angle

Circle one answer.

Nudge (only if you are stuck): Think of where the light must be, and how big its angle of incidence must be.

5. calculate

Supplement. Inside a block of clear plastic of refractive index 1.45, a ray of light meets the flat surface with an angle of incidence of 28°, and passes out into the air. Calculate the angle between the ray in the air and the normal.

Angle between the ray in the air and the normal (°): ______________ unit ________

Nudge (only if you are stuck): Which angle goes on top in the equation, whichever way the light travels? Will the angle in the air be bigger or smaller than 28°?

6. determine

Inside a glass block whose critical angle is 41°, a ray of light meets the top surface. The angle between the ray and the surface is 32°. (a) Determine the angle of incidence. (b) Determine the angle of reflection. (c) The ray is turned so that it meets the surface more steeply. Determine the angle between the ray in the glass and the surface at which the ray in the air runs along the surface.

(a) Angle of incidence (°): ______________ unit ________

(b) Angle of reflection (°): ______________ unit ________

Nudge (only if you are stuck): Angles are measured from the normal, which is at 90° to the surface. Which law does every reflection obey? For (c), what is the angle of incidence when the ray in the air runs along the surface?

7. explain / suggest

In a lit fountain, a lamp under the nozzle shines light up into a smooth jet of water. The jet rises and curves down, and the light stays inside it, so the whole jet glows. (a) Explain why the light stays inside the curved jet. (b) Where the jet breaks up into small drops, light comes out of the water. Suggest why.

(a) Why the light stays in the jet

(b) Why light comes out of the drops

Nudge (only if you are stuck): Where is the light, and what is outside the jet? Compare how sharply the surface curves along a smooth jet and round a small drop.

8. deduce

Binoculars turn the light back through 180° with glass prisms whose angles are 45°, 45° and 90°. Light enters the long face of a prism along the normal, then meets each of the two short faces in turn with an angle of incidence of 45°, and leaves back through the long face. The prism must reflect all of the light at both short faces, with no silver layer. Which material could the prism be made of?

Circle one answer.

A glass with a critical angle of 40°
A plastic with a critical angle of 47°
A plastic with a critical angle of 45°
A resin with a critical angle of 52°

Nudge (only if you are stuck): Total internal reflection needs the angle of incidence to be bigger than the critical angle. Here the angle of incidence is fixed: what does that say about the critical angle?

9. explain / determine

A pupil finds the critical angle of a dense glass with a ray box, a semicircular glass block and an angle scale centred on O, the middle of the flat side. (a) Her partner aims the ray box at a point on the flat side 1 cm to one side of O, instead of at O. Explain why the angle he then reads from the scale is not the true angle of incidence at the flat side. (b) Supplement. Aiming at O, the pupil finds that the ray in the air just runs along the flat side when the angle of incidence is 38°. Determine the refractive index of the glass.

(b) Supplement: Refractive index of the glass: ______________ unit ________

(a) Why the reading is wrong when the ray box is aimed away from O

Nudge (only if you are stuck): For (a): which line from O meets the curved side at 90°, and is the partner’s ray on it? For (b): what is the 38° angle called?

10. calculate

Supplement. The critical angle of sapphire is 34.4°. Calculate the refractive index of sapphire.

Refractive index of sapphire: ______________ unit ________

Nudge (only if you are stuck): Which equation links the critical angle and the refractive index?

11. calculate

Supplement. Cubic zirconia, a sparkling stone used in jewellery, has a refractive index of 2.15. Calculate its critical angle.

Critical angle of cubic zirconia (°): ______________ unit ________

Nudge (only if you are stuck): Find sin c first. Which calculator key turns a sine back into an angle?

12. state

Supplement. Which three are advantages of optical fibres over copper wires for carrying telephone calls and internet data?

Tick every correct statement.

They are cheaper to repair when they break.
One fibre carries far more information at a time.
The signal travels long distances with little loss.
The light is kept inside by a mirror coating.
The light is not affected by electrical interference.
They carry electric current with less resistance.

Nudge (only if you are stuck): Think of how much information they carry, how far, and what electrical interference does to them.

13. explain / predict

Supplement. An optical fibre for telecommunications has a glass core surrounded by a cladding. (a) Explain how light stays inside the core, even where the fibre bends gently. (b) By mistake, a fibre is made with a cladding of higher refractive index than its core. Predict what happens to light in the core when it meets the cladding, and explain why.

(a) How the light stays in the core

(b) A cladding of higher refractive index

Nudge (only if you are stuck): What must be true of the angle of incidence at the side of the core? For (b): in which material does light travel faster, the core or this cladding?

14. describe

Supplement. Put the stages in order to describe how a telephone call travels along an optical fibre.

Write the number of each step in order.

At the far end, the pulses are detected and changed back into an electrical signal.
The electrical signal of the call is coded into very fast pulses of infrared light.
So the pulses travel along the whole fibre, reflected again and again, round gentle bends.
The pulses are sent into one end of the fibre’s core.
Each pulse meets the boundary between the core and the cladding at more than the critical angle and is totally internally reflected.

Step 1: ______
Step 2: ______
Step 3: ______
Step 4: ______
Step 5: ______

Nudge (only if you are stuck): Start with the call as an electrical signal, and end where the signal comes out at the other end.

15. calculate / explain / predict

A diver is under a calm sea. The refractive index of seawater is 1.34. (a) Supplement. Calculate the critical angle of seawater. (b) The diver shines a torch up at the surface, so that the beam meets it with an angle of incidence of 70°. A friend in a boat above sees no light from the torch. Explain why. (If you did not answer (a), take the critical angle of seawater as just under 50°.) (c) The friend then shines a torch down at the sea, so that the beam meets the surface with an angle of incidence of 70° in the air. Predict whether this light gets into the water, and explain why.

(a) Supplement: Critical angle of seawater (°): ______________ unit ________

(b) Why no light reaches the boat, and (c) the beam from the boat

Nudge (only if you are stuck): The sea surface is a boundary between water and air. For each beam, which medium is the light in before it reaches the surface?