Light / optics – part 2 (refraction) Refraction 12.2-12.3 pg 222 – 236

Sub-topics 1) Principles of Refraction 2) Snell’s Law & Refractive Index 3) Total Internal Reflection 4) Optical Fibres

Before We Begin What is this? Who has this at home? A new generation of Internet connection – based on optical fibres. We will study the Physics of optical fibres in this topic.

In Pri School / LSS You might have learned that (1) Light travels in a straight line (2) Speed of light is a constant In this topic, you will learn that both (1) and (2) are INCORRECT Moral of the story: keep your mind open, always be willing to question your teachers, and question what you already think you know.

Refraction Definition: refraction is the bending of light as light passes from one optical medium to another. Similar to reflection, there is an angle of incidence (i) and an angle of refraction (r) (applet) Can you use refraction to explain why white light forms a rainbow when it passes through a prism?

Math lesson! Learn Sine and Arc Sine!

Snell’s Law Snell’s Law is defined as (Sin i)/(Sin r) = constant Sine and Arc Sine will be needed to do calculations for the topic of refraction As previously mentioned, there is an angle of reflection (i) an angle of refraction (r) Snell’s Law is defined as (Sin i)/(Sin r) = constant [verify Snell’s law using applet]

Refractive Index Snell’s Law is very closely related to the concept of “refractive index” Symbol for refractive index is n (no units) Refractive Index is a measure of how fast (or how slow) light passes through a medium There are 3 different ways to define refractive index: First way: n = (speed of light in vacuum) / (speed of light in medium) The first definition is also the “official” definition (in your syllabus)

Refractive Index Hence, n for vacuum or air = 1 n for any other medium >1 Second way: n = (Sin i) / (Sin r) IMPORTANT light MUST be coming from air (vacuum) and going into the medium (e.g. glass, water, etc.) Recall Snell’s Law: (Sin i)/(Sin r) = constant Can you see how they are related? The third way will be discussed in the next sub-topic.

Refractive Index Refractive Index (n) is a property of a material. The same material will always have the same n. [Not in syllabus] Material Refractive Index (n) Vacuum 1 (by definition) Air 1.00027 Water 1.3330 Plastic 1.4 to 1.6 Glass 1.5 to 1.9 Diamond 2.419

Half Time Magic Trick – Disappearing Coin http://www.youtube.com/watch?v=Slas3ik9Lpo Disappearing Glass & Disappearing Gel https://www.youtube.com/watch?v=qH1S83Bkttw

Practice Question If the glass block has a refractive index of 1.5, what is angle x? (hint: need to use arc sine) 60° x

Answer Step 1: Draw Normal! Step 2: i = 90 – 60 = 30° Step 3: Check: light going from air to medium? Ans: Yes! Step 4: Sin i / Sin r = n [IMPORTANT: presentation of working] Sin (30) / Sin r = 1.5 Sin r = Sin (30)/1.5 Sin r = (0.5)/1.5 = 0.3333 (4 sf) r = Sin-1 (0.3333) r = 19.5° (final answer?) No!! Qn ask for x not r!! r = 19.47° (2 dp) x = 90 – r = 90 – 19.47 = 70.5° (1 dp) 30° 60° x r

Some Hints Always draw normal and measure i and r against normal! Light entering at 90° doesn’t bend Light bends towards the normal when it is traveling from lower to higher n Light bends away from the normal when it traveling from higher to lower n If you need to find n, but light is travelling from medium to air, use (sin r)/(sin i) instead of (sin i)/(sin r) [Qn: How come can we do this?]

Even more hints! Sometimes the question uses the term “more dense” or “less dense” This density refers to Optical Density, it is not to be confused with Physical Density (i.e. Mass / Volume) More dense means higher n, less dense means lower n When “less dense” think air When “more dense” think water or glass

Recall from Reflection 1) Straight surface Single Ray 2) Curve surface Single Ray 3) Multiple ray These case studies can also apply to refraction!

Curve Surface Refraction Just like previously in refraction, draw a tangent, and consider angles i and r using the tangent. Special case: semi-circular glass block [applet] Math rule: if a line passes through the center of a circle, it will always be perpendicular to the tangent Note: Semi-circular glass block is a possible lab experiment for light

Multiple Ray Diagram Note: the terms “real depth” and “apparent depth” are not in syllabus But you need to know that the image is more shallow than the object Eye Image Object

Did You Know? [Not in syllabus] Photographers: What is a fish eye lens? Why is it called a “fish eye lens”? Qn: There is a device inside your home (esp if you live in HDB flat) which is also a fish eye lens. What is it? Ans: Doorviewer

Fish-Eye Lens [Not in syllabus] Source: idigitaldarwin.wordpress.com

Try this out 1) Draw a ray diagram of light going from glass to air, n = 1.5, i = 45° What happened? 2) Find the angle of incidence when r = 90° (What did you realize about sin 90?) There is a special name for this angle, it is called the critical angle, or c

Critical Angle (c) Definition: the angle of incidence in an optically denser medium for which the angle of refraction in the optically less dense medium is 90° Third definition of refractive index (n): n = 1 / Sin c Question: what happens when i > c?

Total Internal Reflection (TIR) Important: Something which only occurs when light is going from more dense (i.e. higher n) to less dense (lower n) TIR never occurs when light is going from less dense (lower n) to more dense (higher n) Definition: The complete reflection of a light ray inside an optically denser medium at its boundary with an optically less dense medium [applet demo]

Hints TIR is a case of reflection! That means angle of incidence = angle of reflection applies When ray is going from higher n to lower n, always check for TIR! Remember the two conditions for TIR: From more dense medium to less dense medium Angle of incidence > Critical Angle

Practice Question If the glass block has n = 1.5, complete the ray diagram below: 75°

Answer n = sin i / sin r 1.5 = sin 75 / sin r r = 40.09° [What happens at the top surface?] [Check for TIR!] n = 1/sin c c = 41.8 [Is i>c? Yes] 49.9° 40.1° 75°

Did You Know (pg 234) Periscopes and Binoculars can be constructed either using mirrors (reflection) or using prisms (total internal reflection) Prisms are preferred and is the better method. Qn: Why? Ans: There is double reflection in mirrors due to thickness of glass (remember your lab expt) Important: Textbook Pg 234 has an error! Reward for someone who can spot and explain the error.

Optical Fibre Source: sensorcentral.com

Advantages of Optical Fibre vs Conventional Copper Wire (see textbook Pg 235) Higher carrying capacity Less signal degradation Lightweight Lower cost Can be used as endoscopes for medical purposes

Extra Time! McGyver overcomes the light sensors trap https://www.youtube.com/watch?v=O50bOf_Z2cg The Engineer Guy: How Fiber Optic Cables work http://www.youtube.com/watch?v=0MwMkBET_5I

For further research (1) [Not in syllabus] Qn) Why does light bend when it goes into a different medium? (i.e. what is the actual explanation behind Snell’s law?) Ans: speed of light changes when medium is changed Qn) Why does a change in speed result in the light being bent?

For further research (2) [Not in syllabus] Recall that the n of diamond is very high There are many ways to describe & valuate a diamond. One way is called the “brilliance” of the diamond What is “brilliance” and how is it related to refraction?

Recall - Definitions 3 definitions to memorize in this subtopic! Refraction - is the bending of light as light passes from one optical medium to another. Total Internal Reflection - The complete reflection of a light ray inside an optically denser medium at its boundary with an optically less dense medium Critical Angle - the angle of incidence in an optically denser medium for which the angle of refraction in the optically less dense medium is 90°

Recall - Equations Snell’s Law: (Sin i)/(Sin r) = constant 3 equations for refractive index (n): n = (speed of light in vacuum) / (speed of light in medium) n = (Sin i) / (Sin r), provided light coming from air and going into the medium n = 1 / Sin c, where c is critical angle

Recall - Concepts Refraction as bending of light due to change in medium Less dense to more dense – bend towards the normal More dense to less dense – bend away from the normal Use of Snell’s Law, Sine and Arc Sine to solve refraction problems Critical Angle & Total Internal Reflection Optical Fibres – how it works and its advantages

Personal Card Feedback If you think you have not understood: (a) Principle of Refraction / Snell’s Law – put a colored paper clip on your exit card (b) Total Internal Reflection / Critical Angle / Optical Fiber – put a gold paper clip on your exit card