Copyright © Mark Jordan For non-commercial purposes only….. Enjoy! Refraction 1 Copyright © Mark Jordan Davitt College, Castlebar For non-commercial purposes only….. Enjoy! Comments/suggestions please to the SLSS physics website forum @ http://physics.slss.ie/forum

Help To view contents/show animation on each slide use back/forward ‘arrow keys’ on keyboard mouse click (mouse click must be outside any interactive flash animation area present on a slide) To navigate from slide to slide use navigation buttons provided at bottom-right of each slide To view the ‘flash’ content in this presentation you need to have Shockwave & Flash player installed on your system. If you can see a flashing fish (top right hand corner) then you may proceed….if not click and

Refraction Ray of light travelling from less dense medium (e.g. air) to more dense medium (e.g. glass) changes direction or bends – called Refraction. Angle of incidence Normal i Incident ray A normal (90o) to point where the light enters dense medium (glass) shows ray bending into the normal. Air Glass r Refracted ray Snell, a Dutch mathematician, found that :- Angle of refraction

The Laws of Refraction The incident ray, the normal at the point of incidence and the refracted ray all lie ón the same plane. The ratio of the sin of the angle of incidence to the sine of the angle of refraction is a constant. Refractive index of a medium The refractive index is the ratio of the sine of the angle of incidence to the sine of the angle of refraction when light travels from a vacuum into that medium.

We can verify Snell’s Law with an Experiment Refraction Angle of refraction Light ray travelling from a more dense medium (glass) to a less dense medium (air) bends away from the normal - Snell’s Law again applies i.e. sin i α sin r Normal r Air Glass Refraction is the bending of a wave at the boundary when it is going from one medium to another i We can verify Snell’s Law with an Experiment Angle of incidence

Refractive Index The refractive index between two media – ratio of sin i to sin r when light travels from one media into the other. The order the light passes through the media is important. e.g light passing from glass into water - refractive index = gnw But when light passes from water into glass – refractive index = wng 1 The relation between two is gnw = wng

Refractive Index Example 1 A ray of light enters water from air. If the angle of incidence is 40o find the angle of refraction given n for water is 1.33 Sin i Sin r Sin 400 Sin r Gnw = = = 1.33 Sin 400 1.33 Sin r = = 0.4833 r = Sin-1 (0.4833) = 28.90 Example 2 The refractive index between glass and water is 0.91. What is the refractive index between water and glass? 1 1 Wng = = = 1.1 gnw 0.91

Experiment : To prove Snell's Law i.e sin i / sin r = constant Using a ray box and a block of glass record the values for the angle of incidence & angle of refraction as shown.

i/ o r / o 35o 23o 40o 26o 45o 29o 50o 32o 55o 34o 60o 36o 65o 38o Find the sine of angles of incidence and refraction and record i/ o r / o 35o 23o 40o 26o 45o 29o 50o 32o 55o 34o 60o 36o 65o 38o sin i sin r 0.57 0.39 0.64 0.44 0.7 0.49 0.76 0.53 0.81 0.56 0.86 0.59 0.90 0.62 Draw graph of sin i (y- axis) against sin r (x-axis)

Draw graph of sin i (y-axis) against sin r (x- axis) (0.68, 1.0) Straight line graph through the origin proves Snell’s Law i.e. Sin i  Sin r Slope = k = n (0.14, 0.2) Choose coordinates on line Refractive index (n) = = 1.48

Waves going from air to glass at angle other than 90o Refractive index in terms of relative speed. HONOURS ONLY Waves going from air to glass at angle other than 90o velocity decreases frequency remains constant Wavelength decreases (from c = f λ) In slowing and changing wavelength, the angle at which they proceed MUST change i.e. they REFRACT

Waves going from air to glass at 90o velocity decreases frequency remains constant Wavelength decreases (from c = f λ) If the waves arrive perpendicular to the boundary they do not REFRACT

Total Internal Reflection When a light ray travels from a denser medium into a rarer medium it is refracted away from the normal. As the angle of incidence increases so does the angle of refraction. Eventually the angle i is reached that give an angle r of 90o. The angle i for which this occurs is called the critical angle. C If the angle of incidence is increased beyond the critical angle then all the light is reflected back into the medium and none goes into the 2nd medium. This is called Total internal reflection.

r r= 90° i c i r i Air Air Air Glass Glass Glass light ray travelling from more dense to less dense medium refraction occurs refracted ray bends away from the normal. As the angle of incidence gets bigger, angle of refraction gets bigger & eventually becomes 90o. This angle of incidence is called the critical angle Angle of incidence becomes bigger than the critical angle then.. Total internal reflection occurs

Refractive index and critical angle It is possible to calculate the refractive index using the critical angle r= 90° Air Glass c As the angle of incidence gets bigger, the angle of refraction gets bigger & eventually becomes 90o. This angle of incidence is called the critical angle

Total Internal Reflection and the Critical Angle Example The refractive index of glass is 1.5. Find the critical angle. ang =  Sin C = = = 0.667 1 1 1 Sin C ang 1.5

Critical angle of glass in prism 41.9o (approx) Turning light through 180o using a prism Light from air to glass at 90o No Refraction 450 Light attempting to go from glass to air but angle of incidence greater than critical angle. 450 Total Internal Reflection Light from glass to air at 90o No Refraction

Critical angle of glass in prism 41.9o (approx) Turning light through 90o using a prism Light from air to glass at 90o No Refraction Light attempting to go from glass to air but angle of incidence greater than critical angle. 450 Total Internal Reflection Light from glass to air at 90o No Refraction

Snell's Window Since light can retrace it's path it is found that if light is to enter water from air and arrive at a point below the surface only light within a radius r can reach that point below the surface. This is because any light from the point below the surface that has an angle of incidence greater that the critical angle is reflected back down i.e. Total internal reflection.

Mirage ---- Total Internal Reflection of light from sky A ray of light is continually refracted away from the normal as goes from denser to a rarer medium until the angle of incidence is greater than the cricital angle causeing total internal reflection Light rays from sky Hot air Warm air Low density High density Cool air Hot ground

Refractive index in terms of real and apparent depth An object viewed through a glass block appears to be nearer to you than it really is. The bottom of a swimming pool appears to be less deep that it actually is. The next slide shows why because of refraction an object appears to be less deep that is actually is.

n = Real depth Refractive index in terms of real and apparent depth Glass of water

Refractive index in terms of real and apparent depth It can be proved that the: Refractive index = Real depth Apparent depth Example A block of glass of thickness 4 cm is placed ón a mark ón the bench. When the mark is viewed perpendicularly a virtual image appears 2.67 cm from the top of the glass block. Find the refractive index of the glass. Real depth 4 Apparent depth 2.67 Refractive index = = = 1.5

Finding the refractive index of a liquid using real and apparent depth Pin Apparent depth Mirror Image Water Real depth Cork To find refractive index of a liquid (water) by measuring Real depth over Apparent depth of an object in the liquid.

Optic Fibre another use of total internal reflection Glass cladding of low refractive index Glass core of high refractive index

Total internal reflection and optical fibres Light enters the fibre at an angle greater than the critical angle. Total internal reflection occurs and the ray is reflected in such a way as to ensure continued total internal reflection. Light can in escape if: a) If the fibre is bend at too large an angle. b) If two parts of the optical fibre come in contact with each other. This prevented by coating the fibre with a layer of glass of lower refractive index i.e a rarer or less dense medium.

Uses of optical fibres. Telecommunications -electrical telephone signals are converted to light and travel along optical fibres to their destination. ADVANTAGES Less energy loss than electrical cables Much smaller than electrical wires. Less interference with optical fibres Medicine – optical fibres are used in endoscopes to look at inaccessible parts of the body e.g. stomach. Dentist's drill to carry light near the drill bit and so make it easier to see the work area.