# 25.3 The law of refraction  (Page 4/7)

 Page 4 / 7

## The law of refraction

${n}_{1}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}={n}_{2}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}$

## 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 $\text{30}\text{.}0º$ and the angle of refraction is $\text{22}\text{.}0º$ .

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 ${n}_{1}=1\text{.}\text{00}$ here. From the given information, ${\theta }_{1}=\text{30}\text{.}0º$ and ${\theta }_{2}=\text{22}\text{.}0º$ . With this information, the only unknown in Snell’s law is ${n}_{2}$ , so that it can be used to find this unknown.

Solution

Snell’s law is

${n}_{1}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}={n}_{2}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}.$

Rearranging to isolate ${n}_{2}$ gives

${n}_{2}={n}_{1}\frac{\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}}{\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}}.$

Entering known values,

$\begin{array}{ll}{n}_{2}& =& 1\text{.}\text{00}\frac{\text{sin}\phantom{\rule{0.25em}{0ex}}\text{30}\text{.}0º}{\text{sin}\phantom{\rule{0.25em}{0ex}}\text{22}\text{.}0º}=\frac{0\text{.}\text{500}}{0\text{.}\text{375}}\\ & =& 1.33.\end{array}$

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.

## 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 $\text{30}\text{.}0º$ . Calculate the angle of refraction ${\theta }_{2}$ in the diamond.

Strategy

Again the index of refraction for air is taken to be ${n}_{1}=1\text{.}\text{00}$ , and we are given ${\theta }_{1}=\text{30}\text{.}0º$ . We can look up the index of refraction for diamond in [link] , finding ${n}_{2}=2\text{.}\text{419}$ . The only unknown in Snell’s law is ${\theta }_{2}$ , which we wish to determine.

Solution

Solving Snell’s law for sin ${\theta }_{2}$ yields

$\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}=\frac{{n}_{1}}{{n}_{2}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}.$

Entering known values,

$\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}=\frac{1\text{.}\text{00}}{2\text{.}\text{419}}\text{sin}\phantom{\rule{0.25em}{0ex}}\text{30}\text{.}0º\text{=}\left(0\text{.}\text{413}\right)\left(0\text{.}\text{500}\right)=0\text{.}\text{207}.$

The angle is thus

${\theta }_{2}={\text{sin}}^{-1}0\text{.}\text{207}=\text{11}\text{.}9º.$

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.

## 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 $c=2\text{.}\text{9972458}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}\approx 3\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}.$
• Index of refraction $n=\frac{c}{v}$ , where $v$ is the speed of light in the material, $c$ is the speed of light in vacuum, and $n$ is the index of refraction.
• Snell’s law, the law of refraction, is stated in equation form as ${n}_{1}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}={n}_{2}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}$ .

## 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.

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
What is thermal heat all about
why uniform circular motion is called a periodic motion?.
when a train start from A & it returns at same station A . what is its acceleration?
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
what are the types of radioactivity
Worku
what is static friction
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
definition of mass of conversion
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
Boniface
the range of objects and phenomena studied in physics is
Boniface