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Waves & Optics By: Ahmad Diabmarzouk, Cassandra Stepien, Johanna Kuffner, and Kiera Forsythe     1 

Chapter 1: Waves  

Introduction Energy can be transferred by particles of matter or by waves . Light travels as both a particle and a wave. This is why light can both reflect and refract. Waves can be categorized in many different ways, from how they are composed to how they travel. Mechanical Waves are waves that need a medium to travel through. They use the vibration of particles of the medium that they are travelling through. Electromagnetic Waves do not need something to travel as they move on their own. Examples: Mechanical Waves Water waves Sound waves Electromagnetic Waves Microwaves Radio waves Light X-Rays Different types of Mechanical waves are longitudinal waves and transverse waves. The difference is that the vibration of the medium is parallel to the energy flow or wave direction for longitudinal waves. Longitudinal waves are composed of compressions and rarefactions. While for transverse waves the vibration of the medium is perpendicular to the energy flow or wave 8. Surface waves are a


combination of transverse and longitudinal waves. It is a simple harmonic motion; better known as repeated vibration.

Figure 1.1.1 - Is a diagram of transverse waves.

Figure 1.1.2 - Is an diagram of longitudinal waves.

Did You Know? Sound travels as a longitudinal wave.

Definitions: Here are a few key terms to keep in mind Before we start working on more complicated topics: λ - Also known as lambda (λ = wavelength) is the shortest distance from two in phase points along a wave. Crest - Maximum displacement of a medium. Trough - Maximum displacement of a medium, in the opposite direction. Pulse - A single disturbance (one bump). Wavelength - The shortest distance between two adjacent points. In Phase - Two points In a medium vibrating the same direction, together. Out of Phase - Two points in a medium NOT vibrating together.


Amplitude - Maximum displacement from equilibrium position. Wave properties - Constructive and destructive interference, diffraction, and polarization can only occur with waves (not particles). These characteristics of light give support to the wave nature of light. Refraction - Change in wave direction that occurs at the boundaries of two mediums. Constructive interference - When a crest from one source meets a crest from another source; the energies add to displace the medium. Destructive interference - When a crest and a trough meet, the energies still add but they tend to cancel out. Node - Two waves travelling in opposite directions always interfere destructively (no displacement). Antinode - Points midway between nodes where they interfere constructively (maximum displacement occurs here). Diffraction - The spreading out of a wave as it passes through a small opening around an obstacle. Frequency - the rate at which a vibration occurs that constitutes a wave, either in a material, or in a electromagnetic field, usually measured per second.


Starting with Equations Now that we know a few of our key definitions we can start to move onto equations, the first basic equation is: v=λf This formula is the same as one we learnt in previous units,V=d/t : ● v stands for velocity(m/s) ● λ stands for the wavelength(m) ● f stands for the frequency(Hz)

f=1 T or f = # of times S ● T stands for the period(s) or Time ● S stands for seconds

Example #1: A wave has a wavelength of 4.5m and a frequency of 3.9Hz. What is the speed of the wave? v= λf v = (4.5m)(3.9Hz) v= 17.55m/s v= 17.6m/s Tip: Remember to use your sig figs and proper units to get full marks for the day when the test arrives!


Example #2 A wave with a speed of 50m/s has a wavelength of 9.5m. What is the period? Part 1 of example 2: v=λf 50m/s = (9.5m)(f) 50m/s / 9.5m = (9.5m)(f) / 9.5m 5.26Hz = f 5.3Hz = f

Part 2 of example 2: T = 1f T = 1(5.26Hz) T = 5.26s Practice Questions: 1) Which graph in figure 1.3 shows two points that are in phase?

2) A wave has a frequency of 2.10Hz and a wavelength of 5.30m. what is the speed?

3) 25 crests are seen to pass a single point in 5.0s. what is the frequency of the wave


4) A light has a speed of 3.00x 108 m/s. If the length of the wave is 5.00x 10−7 m, what is the period?  

ANSWERS: 1) A 2) 11.1m/s 3) 5.0Hz 4) 1.67x 10−15 s 

Lab Time! Here’s a wave lab for you to complete:

Light can be studied under two general categories: i) Ray Diagrams Ray diagrams can be used for many reasons such as to describe reflection and refraction, and they even aim some “light on the particle/wave nature of light” ● Reflections have barriers

● Refractions have boundaries


ii) Wave Properties Constructive and destructive interference, polarization and diffraction can only exist with waves(not particles). The characteristics of the light give support to the wave’s nature of light. Reflection Law of Reflection When a ray of light is reflected of a plain mirror the reflection will be equal to the incidence. The angle of incidence = The angle of reflection ∠i = ∠r Types of Reflection: Regular Reflection ● Occurs on smooth surfaces ● Parallel light rays are reflected parallel

Diffuse Reflection ● Occurs on a rough surface ● Light is reflected in many directions ● Law of reflection still applies


Refraction Instead of being reflected off the same medium, Refraction deals with when a ray of light enters a new medium. Each time a ray of light enters a new medium it changes it’s speed(v) and direction(θ), although the frequency(f) and period(T) never change during a refraction.

Figure 1.1.5

Did You Know? That Snell’s Law is another name for the Law of Refraction!


Law of Refraction(Snell’s law):

● ● ● ●

θ 1 represents the angle of incidence θ 2 represents the angle refraction n is the index of refraction, n1 is medium 1 and n2 is medium 2 λ is the wave length Tip #1: the only characteristic that can change during refraction are the velocity and the wavelength. Frequency does not change during refraction. Tip #2: Remember LISA and SLIT. Lisa means that if the index of refraction is Larger to Smaller then the angle of refraction is further Away from the normal. Slit means that if index of refraction is Smaller to Larger than the angle of refraction is closer To the normal

Example: A ray of light strikes the surface of a block of glass(n=1.50) and has an incident angle of 72 º  what is the angle of refraction? sin 72 º =   1.50 sin θ 2   1.00

sin 72 º  = 1.50( sin θ 2  )

sin 72 º  = sin θ 2   1.50


sin  −1  (sin 72 º /1.50)=   θ 2  

θ 2 =39.3 º

Practice Questions Tip: The index of refraction of air is 1.00

1) A ray of light travels from air into water (1.33) and then into glass (1.50) as shown in the diagram. find the angle of refraction in the glass. the ray is 35.0 º  to the water.

2) A ray of light that strikes the surface of the water (n=1.33) at an angle of 60.0 º  from the water surface. what is the angle of refraction?

3) What is the index of a substance if the angle of incidence is 53.0 º  and the angle of refraction is 41.0?

4) what is the frequency of the light in a diamond (n=2.42) if the frequency in air is 6.20x10¹⁴ Hz


the speed of light in a clear liquid is 2.3x10⁸ m/s what is the index of refraction?

Tip: The speed of light in air is 3.00x10⁸ m/s

6) Monochromatic light has a wavelength of 5.75x10  −7  m in air and 4.32x10  −7  m in a clear liquid. If a ray of light enters this clear liquid at an incident angle of 25.0 º ,  what is the angle of refraction?

ANSWERS: 1) 33.1 º  2) 22.1 º  3) 1.22

4) 6.20x10¹⁴ Hz, frequency does not change     11 

5) 1.30 6) 18.5 º  


Diffraction Diffraction is when a wave is spreading out as it passes a small opening or around an obstacle.

Did You Know That only waves refract and particles do not.

Wave Effects i) Doppler effect The Doppler effect occurs when a source that is generating waves moves towards an observer, the frequency of the wave relative to the observer increases. When the source moves away from the observer, the frequency of the wave relative to the observer decreases.              

Fun Fact The Doppler effect is used in short-range radar devices and weather tracking devices.  


ii) Scattering  Scattering occurs when waves hit an obstacle that is smaller than the wavelength of the wave. When this happens, waves are scattered from the obstacle into multiple directions. The amount of scattering also depends on the wavelengths of the incident waves. Ever wondered why the sky is blue? The sky is blue becauses the atmosphere contains many particles such as nitrogen and oxygen, which act as obstacles to sunlight. BLue light has a short wavelength compare to red light, therefore it is scattered more. the sky looks blue because blue light has been scattered in all directions by the particles in the atmosphere. Tip: Shorter wavelengths are scattered more than longer ones.  


Waves reflected from a Barrier or Boundary: When a wave hits a boundary, some of the energy is transmitted into the new medium while some is reflected. The pulse that passes into the new medium is always erect. The pulse that bounces off the new medium is reflected.

i) Two densities & unfixed end ● the transmitted pulse is always erect ● the reflected pulse that occurs from a less dense medium to a more dense medium is always inverted ii) One density & a fixed end ● the reflected pulse, that is produced from a fixed end is both inverted and reversed

iii) One density & a unfixed end ● the reflected pulse produced by an unfixed end is reversed       

Figure 1.2.1 Extra Fun Check out this link for an interactive learning experience with waves. 



Chapter 2: Optics Introduction Throughout the Optics chapter, we start to talk about mirrors & lens. This includes both convex and concave mirrors and lens. For both mirrors and lenses all virtual images are always erect and all real images are always inverted. Definitions Concave mirror - reflects light rays causing rays to converge or come together at focal point. Convex mirror - Reflects light from surface causing rays to diverge or spread apart from focal point. Center of curvature(C) - The point that is the distance of the radius from the mirror. Principle focus(F) - The point where reflected rays converge to or diverge from. Focal length(f) - Distance between mirror and F (half the radius). Spherical aberration - When using a spherical mirror, light rays do not converge or diverge exactly at F causing spherical aberration. To eliminate this problem a parabolic mirror is used. Convex - Convex mirrors are curved outward. Concave - Concave mirrors are curved inwards.     16 

Principle Axis - Centre line. Vertex - Where the mirror meets the principle axis (center of mirror). Radius of Curvature - Distance from (C)to the vertex. Focal point(F) - Half the distance between (C)and the vertex. Focal length - Distance from the focal point (f) to the vertex. do - Distance to the object. di - Distance to the image. ho - Height of the object. hi - Height of the image. Concave lens - can be called diverging lens when light passes through it. It is any lens that is thinner at the centre than at the edges. Convex lens - can be called converging lens when light passes through it. It is any lens that is thicker at the centre than at the edges. Lenses - used to change the direction of light by refraction.


Chromatic aberration - when different coloured components of light passes through a lens or is refracted differently, causing the object to"appear" to be"ringed" in a given colour.

Real Images vs Virtual Images Real Images ● Produced in front of a mirror when light rays converge ● Can be projected onto a screening ● Usually inverted

Virtual Images ● Light rays do not converge ● Can not be projected onto a screen ● Usually erect ● Appear to be BEHIND THE MIRROR

Concave Mirrors Think of concave mirrors as the shape of a curved cave. All concave mirrors use a real focal point. Concave mirrors are also short for converging mirrors.


Steps on How to Draw the Ray Diagrams of Concave Mirrors Part I: If the object is outside of the focal point(to the left of the focal point) here is how you would draw it.

You now know we’re you’re image is created when the object is outside the focal point! Part II: If the object is inside the focal point(to the right) then here is how you would draw it.


Figure 2.1.3

  Convex Mirrors Think of convex mirrors as the shape of a baby bump, the opposite shape of a concave mirror. All convex mirrors also use a virtual point. Convex mirrors are also short for diverging mirrors.     20 

Did You Know? That convex mirrors always produce smaller, virtual and erect images!

Steps on How to Draw the Ray Diagrams of Convex Mirrors Part I: How to draw Convex Mirrors, no matter where the object is.


Total Internal Reflection: Total internal reflection is the effect that occurs when an angle of incidence exceeds the critical angle. When this happens all of the incident light is reflected back into the medium, and the angle of refraction in this case is 90 degrees. Total internal reflection only occurs when light passes into a less dense medium. Knowing the Details Real images that are inverted


Virtual images that are erect


Real images that are formed in front of the mirror


Virtual images that are formed behind the mirror


Always positive


Positive for concave mirrors


Negative for concave mirrors


Positive for convex mirrors


Negative for convex mirrors


Tip:Object at F produces NO IMAGE.

Lab Time! Here’s a mirror lab for you to complete:


Lenses Lenses are used to change the direction of light by refraction. there are two types of lenses; convex and concave. Unlike mirrors, the focal point for lenses can occur on either side of the lens and "C" does not exist. While "C" is used for mirrors, "F" and "2F" is used for lenses. For lenses, it will be the curvature of the lens and the index of refraction (n) that will determine where the focal point (F) will be. Fun Fact Chromatic aberration is when different coloured components of light passing through a lens are refracted differently, causing the object to appear to be “ringed” in a given colour. In order to eliminate this problem, an achromatic lens is used; an achromatic lens is a converging lens joined to a diverging lens.

Concave Lenses A concave lens can also be called a diverging lens, because the light spreads out as it passes through it. You can easily recognize these lenses because they are thinner at the centre and fatter at the edges. These lenses will always produce a virtual, erect and smaller image.


Did you know? Concave lenses are used to correct nearsightedness.

Convex Lenses A convex lens can also be called a converging lens, because the rays of light that pass through the mirror come together. These lenses are thicker at the centre than at the edges; opposite to a concave lens.

Did You Know? Convex lenses are used in microscopes, telescopes, and magnifying glasses. They are also used as lenses in glasses (or contacts) to correct farsightedness.

Polarization     24 

Polarization is a property of waves that can move in more than one direction. Longitudinal waves cannot be polarized while transverse waves can. Since light, if it was wavelike, acts like a transverse wave, it too can be polarized.

Transverse waves can vibrate in any direction except when it comes in contact with a filter that will only allow it to move in one direction. When this happens we know we have polarized the light wave.

Did You Know? The most popular use for polarization is sunglasses; it reduces the glare off horizontal surfaces.

Figure 2.6     25 

Reflections from Curved Mirrors

Example A glowing object 4.0 cm tall is placed 9.0cm from a concave lens. If the lens has a focal length of 5.0cm, what is the distance of the image from the lens? 1/f = 1/di + 1/do → 1/-5 = 1/di + 1/9 -0.2 = 1/di + 0.11 -0.11 -0.11 1/di = -0.31 di = 3.2cm

Practice Questions 1. A glowing object 6.0 cm tall is placed 9.0cm from a convex lens. If the lens has a focal length of 8.0cm, what is the distance of the image from the lens? 2. A glowing object 5.0 cm tall is placed 4.5cm from a concave lens. If the lens has a focal length of 4.5cm, what is the distance of the image from the lens? 3. A glowing object 3.0 cm tall is place 6.0 cm from the concave lens. If a virtual image is produced that is 1.0 cm tall, what is the focal length of the lens?     26 

4. A glowing object 2.0 cm tall is placed 5.0 cm from a lens. If a virtual image is produced that is 4.0 cm tall, what is the focal length of the lens? 5. A concave lens produces an image that is 2.5 cm from the lens. If the focal length of the lens is 6.0 cm, at what distance from the lens is the object?

Answers 1. +72 cm 2. -2.3cm 3. -3.0cm 4. 10cm 5. 4.3cm

The Math of Curved Mirrors hi = -di = m (magnification) ho = -di Tip: If forgotten the meanings of the terms refer to page 22 under Knowing The Details

Some helpful tips ● Erect images: +Hi ● Inverted Images: -Hi ● A negative value of magnification signifies that the image will be inverted.

Practice Questions 1. An object is 30.0cm in front of a concave mirror. This concave mirror has a focal length of 15.0 cm high. How high is the image produced? 2.What is the diameter of the image if the object placed in front of a concave mirror. The object has a diameter of 3.0cm and a length of 1.8 cm high. 3. A mirror with a radius of 40mm is used, if it is a concave mirror and it is used 16 mm from an object what is the magnification of the object? Answers: 1.) 30cm 2.) 24cm 3.)5.0cm


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Waves & Optics Textbook