13.4 Total internal reflection

The main part of an endoscope is the optical fibre. Light is shone down the optical fibre and a medical doctor can use the endoscope to look inside a patient. Endoscopes are used to examine the inside of a patient's stomach, by inserting the endoscope down the patient's throat.

Endoscopes allow minimally invasive surgery. This means that a person can be diagnosed and treated through a small incision. This has advantages over open surgery because endoscopy is quicker and cheaper and the patient recovers more quickly. The alternative is open surgery which is expensive, requires more time and is more traumatic for the patient.

Total internal reflection and fibre optics

1. Describe total internal reflection, referring to the conditions that must be satisfied for total internal reflection to occur.
   
2. Define what is meant by the critical angle when referring to total internal reflection. Include a ray diagram to explain the concept.
   
3. Will light travelling from diamond to silicon ever undergo total internal reflection?
   
4. Will light travelling from sapphire to diamond undergo total internal reflection?
   
5. What is the critical angle for light traveling from air to acetone?
   
6. Light traveling from diamond to water strikes the interface with an angle of incidence of 86 ${}^{\circ }$ . Calculate the critical angle to determine whether the light be totally internally reflected and so be trapped within the water.
   
7. Which of the following interfaces will have the largest critical angle?
   1. a glass to water interface
   2. a diamond to water interface
   3. a diamond to glass interface
8. If the fibre optic strand is made from glass, determine the critical angle of the light ray so that the ray stays within the fibre optic strand.
   
9. A glass slab is inserted in a tank of water. If the refractive index of water is 1,33 and that of glass is 1,5, find the critical angle.
   
10. A diamond ring is placed in a container full of glycerin. If the critical angle is found to be 37,4 ${}^{\circ }$ and the refractive index of glycerin is given to be 1,47, find the refractive index of diamond.
    
11. An optical fibre is made up of a core of refractive index 1,9, while the refractive index of the cladding is 1,5. Calculate the maximum angle which a light pulse can make with the wall of the core. NOTE: The question does not ask for the angle of incidence but for the angle made by the ray with the wall of the core, which will be equal to 90 ${}^{\circ }$ - angle of incidence.
    

Summary

1. We can see objects when light from the objects enters our eyes.
2. Light rays are thin imaginary lines of light and are indicated in drawings by means of arrows.
3. Light travels in straight lines. Light can therefore not travel around corners. Shadows are formed because light shines in straight lines.
4. Light rays reflect off surfaces. The incident ray shines in on the surface and the reflected ray is the one that bounces off the surface. The surface normal is the perpendicular line to the surface where the light strikes the surface.
5. The angle of incidence is the angle between the incident ray and the surface, and the angle of reflection is the angle between the reflected ray and the surface.
6. The Law of Reflection states the angle of incidence is equal to the angle of reflection and that the reflected ray lies in the plane of incidence.
7. Specular reflection takes place when parallel rays fall on a surface and they leave the object as parallel rays. Diffuse reflection takes place when parallel rays are reflected in different directions.
8. Refraction is the bending of light when it travels from one medium to another. Light travels at different speeds in different media.
9. The refractive index of a medium is a measure of how easily light travels through the medium. It is a ratio of the speed of light in a vacuum to the speed of light in the medium. $n=\frac{c}{v}$
10. Snell's Law gives the relationship between the refractive indices, angles of incidence and reflection of two media. $n_{1}sin{\theta }_1=n_{2}sin{\theta }_2$
11. Light travelling from one medium to another of lighter optical density will be refracted towards the normal. Light travelling from one medium to another of lower optical density will be refracted away from the normal.
12. Objects in a medium (e.g. under water) appear closer to the surface than they really are. This is due to the refraction of light, and the refractive index of the medium. $n=\frac{\mathrm{real}\mathrm{depth}}{\mathrm{apparent}\mathrm{depth}}$
13. Mirrors are highly reflective surfaces. Flat mirrors are called plane mirrors. Curved mirrors can be convex or concave. The properties of the images formed by mirrors are summarised in Table 3.2.
14. A real image can be cast on a screen, is inverted and in front of the mirror.A virtual image cannot be cast on a screen, is upright and behind the mirror.
15. The magnification of a mirror is how many times the image is bigger or smaller than the object. $m=\frac{\mathrm{image}\mathrm{height}\left({\mathrm{h}}_{\mathrm{i}}\right)}{\mathrm{object}\mathrm{height}\left({\mathrm{h}}_0\right)}$
16. The critical angle of a medium is the angle of incidence when the angle of refraction is ${90}^{\circ }$ and the refracted ray runs along the interface between the two media.
17. Total internal reflection takes place when light travels from one medium to another of lower optical density. If the angle of incidence is greater than the critical angle for the medium, the light will be reflected back into the medium. No refraction takes place.
18. Total internal reflection is used in optical fibres in telecommunication and in medicine in endoscopes. Optical fibres transmit information much more quickly and accurately than traditional methods.

Exercises

1. Give one word for each of the following descriptions:
   1. The image that is formed by a plane mirror.
   2. The perpendicular line that is drawn at right angles to a reflecting surface at the point of incidence.
   3. The bending of light as it travels from one medium to another.
   4. The ray of light that falls in on an object.
   5. A type of mirror that focuses all rays behind the mirror.
2. State whether the following statements are TRUE or FALSE. If they are false, rewrite the statement correcting it.
   1. The refractive index of a medium is an indication of how fast light will travel through the medium.
   2. Total internal refraction takes place when the incident angle is larger than the critical angle.
   3. The magnification of an object can be calculated if the speed of light in a vacuum and the speed of light in the medium is known.
   4. The speed of light in a vacuum is about $3\times {10}^8$ m.s ${}^{-1}$ .
   5. Specular reflection takes place when light is reflected off a rough surface.
3. Choose words from Column B to match the concept/description in Column A. All the appropriate words should be identified. Words can be used more than once.

   	Column A	Column B
   (a)	Real image	Upright
   (b)	Virtual image	Can be cast on a screen
   (c)	Concave mirror	In front
   (d)	Convex mirror	Behind
   (e)	Plane mirror	Inverted
   		Light travels to it
   		Upside down
   		Light does not reach it
   		Erect
   		Same size

   
   
4. Complete the following ray diagrams to show the path of light.

   

   

   

   

   

   

5. A ray of light strikes a surface at 35 ${}^{\circ }$ to the surface normal. Draw a ray diagram showing the incident ray, reflected ray and surface normal. Calculate the angles of incidence and reflection and fill them in on your diagram.
   
6. Light travels from glass (n = 1,5) to acetone (n = 1,36). The angle of incidence is 25 ${}^{\circ }$ .
   1. Describe the path of light as it moves into the acetone.
   2. Calculate the angle of refraction.
   3. What happens to the speed of the light as it moves from the glass to the acetone?
   4. What happens to the wavelength of the light as it moves into the acetone?
   5. What is the name of the phenomenon that occurs at the interface between the two media?
   
   
7. A stone lies at the bottom of a swimming pool. The water is 120 cm deep. The refractive index of water is 1,33. How deep does the stone appear to be?
   
8. Light strikes the interface between air and an unknown medium with an incident angle of 32 ${}^{\circ }$ . The angle of refraction is measured to be 48 ${}^{\circ }$ . Calculate the refractive index of the medium and identify the medium.
   
9. Explain what total internal reflection is and how it is used in medicine and telecommunications. Why is this technology much better to use?
   
10. A candle 10 cm high is placed 25 cm in front of a plane mirror. Draw a ray diagram to show how the image is formed. Include all labels and write down the properties of the image.
    
11. A virtual image, 4 cm high, is formed 3 cm from a plane mirror. Draw a labelled ray diagram to show the position and height of the object. What is the magnification?
    
12. An object, 3 cm high, is placed 4 cm from a concave mirror of focal length 2 cm. Draw a labelled ray diagram to find the position, height and properties of the image.