1. Home
  2. College physics
  3. Geometric optics
  4. The law of refraction

25.3 The law of refraction  (Page 4/7)

<< Chapter < Page
  College physics     Page 4 / 7
Chapter >> Page >

The law of refraction

n 1 sin θ 1 = n 2 sin θ 2 size 12{n rSub { size 8{1} } "sin"θ rSub { size 8{1} } =n rSub { size 8{2} } "sin"θ rSub { size 8{2} } } {}

Take-home experiment: a broken pencil

A classic observation of refraction occurs when a pencil is placed in a glass half filled with water. Do this and observe the shape of the pencil when you look at the pencil sideways, that is, through air, glass, water. Explain your observations. Draw ray diagrams for the situation.

Determine the index of refraction from refraction data

Find the index of refraction for medium 2 in [link] (a), assuming medium 1 is air and given the incident angle is 30 . 0º size 12{"30" "." 0°} {} and the angle of refraction is 22 . 0º size 12{"22" "." 0°} {} .

Strategy

The index of refraction for air is taken to be 1 in most cases (and up to four significant figures, it is 1.000). Thus n 1 = 1 . 00 size 12{n rSub { size 8{1} } =1 "." "00"} {} here. From the given information, θ 1 = 30 . 0º size 12{q rSub { size 8{1} } ="30" "." 0°} {} and θ 2 = 22 . 0º size 12{q rSub { size 8{2} } ="22" "." 0°} {} . With this information, the only unknown in Snell’s law is n 2 size 12{n rSub { size 8{2} } } {} , so that it can be used to find this unknown.

Solution

Snell’s law is

n 1 sin θ 1 = n 2 sin θ 2 . size 12{n rSub { size 8{1} } "sin"θ rSub { size 8{1} } =n rSub { size 8{2} } "sin"θ rSub { size 8{2} } } {}

Rearranging to isolate n 2 size 12{n rSub { size 8{2} } } {} gives

n 2 = n 1 sin θ 1 sin θ 2 . size 12{n rSub { size 8{2} } =n rSub { size 8{1} } { {"sin"θ rSub { size 8{1} } } over {"sin"θ rSub { size 8{2} } } } } {}

Entering known values,

n 2 = 1 . 00 sin 30 . 0º sin 22 . 0º = 0 . 500 0 . 375 = 1.33. alignl { stack { size 12{n rSub { size 8{2} } =1 "." "00" { {"sin""30" "." 0°} over {"sin""22" "." 0°} } = { {0 "." "500"} over {0 "." "375"} } } {} #=1 "." "33" "." {} } } {}

Discussion

This is the index of refraction for water, and Snell could have determined it by measuring the angles and performing this calculation. He would then have found 1.33 to be the appropriate index of refraction for water in all other situations, such as when a ray passes from water to glass. Today we can verify that the index of refraction is related to the speed of light in a medium by measuring that speed directly.

Got questions? Get instant answers now!

A larger change in direction

Suppose that in a situation like that in [link] , light goes from air to diamond and that the incident angle is 30 . 0º size 12{"30" "." 0°} {} . Calculate the angle of refraction θ 2 size 12{q rSub { size 8{2} } } {} in the diamond.

Strategy

Again the index of refraction for air is taken to be n 1 = 1 . 00 size 12{n rSub { size 8{1} } =1 "." "00"} {} , and we are given θ 1 = 30 . 0º size 12{q rSub { size 8{1} } ="30" "." 0°} {} . We can look up the index of refraction for diamond in [link] , finding n 2 = 2 . 419 size 12{n rSub { size 8{2} } =2 "." "419"} {} . The only unknown in Snell’s law is θ 2 size 12{q rSub { size 8{2} } } {} , which we wish to determine.

Solution

Solving Snell’s law for sin θ 2 size 12{q rSub { size 8{2} } } {} yields

sin θ 2 = n 1 n 2 sin θ 1 . size 12{"sin"θ rSub { size 8{2} } = { {n rSub { size 8{1} } } over {n rSub { size 8{2} } } } "sin"θ rSub { size 8{1} } } {}

Entering known values,

sin θ 2 = 1 . 00 2 . 419 sin 30 . 0º = ( 0 . 413 ) ( 0 . 500 ) = 0 . 207 . size 12{"sin"q rSub { size 8{2} } = { {1 "." "00"} over {2 "." "419"} } "sin""30" "." 0"°=" left (0 "." "413" right ) left (0 "." "500" right )=0 "." "207"} {}

The angle is thus

θ 2 = sin − 1 0 . 207 = 11 . 9º . size 12{θ rSub { size 8{2} } ="sin" rSup { size 8{ - 1} } 0 "." "207"="11" "." 9°} {}

Discussion

For the same 30º angle of incidence, the angle of refraction in diamond is significantly smaller than in water ( 11.9º rather than 22º —see the preceding example). This means there is a larger change in direction in diamond. The cause of a large change in direction is a large change in the index of refraction (or speed). In general, the larger the change in speed, the greater the effect on the direction of the ray.

Got questions? Get instant answers now!

Section summary

  • The changing of a light ray’s direction when it passes through variations in matter is called refraction.
  • The speed of light in vacuum c = 2 . 9972458 × 10 8 m/s ≈ 3 . 00 × 10 8 m/s . size 12{c=2 "." "9972458" times "10" rSup { size 8{8} } " m/s" approx 3 "." "00" times "10" rSup { size 8{8} } " m/s"} {}
  • Index of refraction n = c v size 12{n= { {c} over {v} } } {} , where v size 12{v} {} is the speed of light in the material, c size 12{c} {} is the speed of light in vacuum, and n size 12{n} {} is the index of refraction.
  • Snell’s law, the law of refraction, is stated in equation form as n 1 sin θ 1 = n 2 sin θ 2 size 12{n rSub { size 8{1} } "sin"θ rSub { size 8{1} } =n rSub { size 8{2} } "sin"θ rSub { size 8{2} } } {} .

Conceptual questions

Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.

Got questions? Get instant answers now!

Questions & Answers

what is phylogeny
Odigie Reply
evolutionary history and relationship of an organism or group of organisms
AI-Robot
ok
Deng
what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 2

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask