# Snell’s law example 1 | Geometric optics | Physics | Khan Academy

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As promised, let’s do a couple

of simple Snell’s law examples. So let’s say, that

I have two media– I guess the plural of mediums. So let’s say I have

air right here. And then right here

is the surface. Let me do that in a

more appropriate color. That is the surface

of the water. And I know that I have a light

ray, coming in with an incident angle of– so relative to the

perpendicular– 35 degrees. And what I want to know is

what the angle of refraction will be. So it will refract a little bit. It will bend inwards

a little bit, since this outside’s going to

be in the air a little longer, if you buy into my car

travelling into the mud analogy. So it will then

bend a little bit. And I want to figure out

what this new angle will be. I want to figure out

the angle of refraction. I’ll call that theta 2. What is this? This is just straight

up applying Snell’s law. And I’m going to use the

version using the refraction indices, since we

have a table here from the ck12.org FlexBook

on the refraction indices– and you can go get it

for free if you like. And that just tells

us that the refraction index for the

first medium– that is air– times the sine of the

incident angle, in this case is 35 degrees, is going to

be equal to the refraction index for water, times the

sine of this angle right over here– times

the sine of theta 2. And we know what the refraction

index for air and for water is, and then we just have

to solve for theta 2. So let’s just do that. The refraction index for

air is this number right over here, 1.00029. So it’s going to be, there’s

three 0’s, 1.00029 times the sine of 35 degrees, is going

to be equal to the refraction index for water, which is 1.33. So it’s 1.33 times

sine of theta 2. Now we can divide both sides

of this equation by 1.33. On this side, we’re just left

with the sine of theta 2. On the left-hand side, let’s

get our calculator out for this. So let me get the

handy calculator. And so we want to

calculate– and I made sure my calculator is in degree

mode– 1.00029 times the sine of 35

degrees, so that’s the numerator of

this expression right here– the green part–

that’s 0.5737 divided by 1.33. I’m just dividing by

the numerator here. When you just

divide this answer, it means your last answer. That’s the numerator up here

divided by that denominator. And so I get 0.4314. I’ll just round a little bit. So I’ll get– I’ll

switch colors– 0.4314 is equal to

sine of theta 2. And now to solve

for theta, you just have to take the inverse

sine of both sides of this. This doesn’t mean sine

to the negative 1. You could also use the arcsine. The sine inverse

of 0.4314 is going to be equal to– the inverse

sine of sine is just the angle itself or, I guess

when we’re dealing with angles in a

normal range, it’s going to be the angle itself. And that’s going to be the

case with this right over here. And if any of that

is confusing you might want to review the

videos on the inverse sine and the inverse

cosine, and they’re in the Trigonometry playlist. But we can very

easily figure out the inverse sine for

this right over here. You literally, you

have sine here, when you press Second

you get the inverse sine. So it’s the inverse

sine, or the arcsine of that number right over there. And instead of

retyping it, I can just put Second, and then Answer. So I’m taking the inverse

sine of that number. And that will give me an angle. And I get 25.55, or I’ll

round it, 25.6 degrees. So this theta 2,

is equal to 25.6, or I’ll say approximately

equal to some 25.6 degrees. So Snell’s law goes

with our little car driving in to the mud analogy. It’s going to be

a narrow degree. It’s going to come inwards a

little bit closer to vertical. And theta 2 is equal

to 25.6 degrees. And you could do the other way. Let’s do another example. Let’s say that we have,

just to make things simpler, that I have some

surface right over here. So this is some

unknown material. And we’re traveling in space,

we’re on the space shuttle, and so this is a vacuum. Or pretty darn

close to a vacuum. And I have light coming in at

some angle, just like that. Let me drop a vertical. So it’s coming in at some angle. Actually, let me

make it interesting. Let me make the light go

from the slower medium to the faster medium, just

because the last time we went from the faster

to the slower. So it’s in a vacuum. So let’s say I have some

light traveling like this. And once again, just to get

the “get” of whether it’s going to bend inward

or bend outward, the left side is going

to get out first, so is going to

travel faster first. So it will bend inwards when it

goes into the faster material. So this is some unknown. This is some unknown material,

where light travels slower. And let’s say we were able

to measure, the angles. So let me drop a

vertical right here. And so let’s say that this

right here, is 30 degrees. And let’s say we’re

able to measure the angle of refraction. And the angle of

refraction over here is, let’s say that

this is 40 degrees. So given that we’re able

to measure the incident angle, and the

angle of refraction, can we figure out the refraction

index for this material? Or even better, can we

figure out the speed of light in that material? So let’s figure out the

refraction index first. So we know the refraction index

for this questionable material times the sine of

30 degrees is going to be equal to the refraction

index for a vacuum. Well, that’s just the

ratio of the speed of light in the vacuum to the

speed of light in the vacuum. So that’s just going to be 1. This is the same thing

as n for a vacuum– and I’ll just write a 1 there–

times the sine of 40 degrees. Or If we wanted to solve for

this unknown refraction index, we just divide both sides of

the equation by sine of 30. So our unknown

refraction index is going to be– this is

just the sine of 40 degrees– over this– over

the sine of 30 degrees. So we can get our

handy calculator out. And so we have the

sine of 40 divided by the sine of 30 degrees. Make sure you’re in degree

mode, if you try this. And you get, let’s

just round it, 1.29. So this is approximately equal

to– so our unknown refraction index for our material

is equal to 1.29. So we were able to figure out

the unknown refraction index. And we can actually

use this to figure out the velocity of light

in this material. Because remember, this

unknown refraction index is equal to the

velocity of light in a vacuum, which is 300

million meters per second, divided by the velocity in this

material, the unknown material. So we know that 1.29 is equal

to the velocity of light in a vacuum. So we could write

300 million meters per second, divided by

the unknown velocity in this material. I’ll put a question mark. And so we can

multiply both sides times our unknown velocity. I’m running out of

space over here, I have other stuff

written over here. So I could multiply

both sides by this v and I’ll get 1.29 times

this v with a question mark, is going to be equal to 300

million meters per second. And then I could divide

both sides by 1.29. v question mark is going to be

this whole thing, 300 million divided by 1.29. Or another way to

think of it is, light travels 1.29

times faster in a vacuum than it does in this

material right over here. But let’s figure

out it’s velocity. So in this material,

light will travel a slow– so the 300 million

divided by 1.29. Light will travel a super slow

232 million meters per second. So this is approximately,

just to round off, 232 million meters per second. And if we had to guess

what this material is, let’s see– I just

made up these numbers– but let’s see if there’s

something that has a refraction index close to 1.29. So that’s pretty

close to 1.29 here. So maybe this is some

type of interface with water in a vacuum,

where the water somehow isn’t actually

evaporating because of the lack of pressure. Or maybe it’s some

other material. Let’s keep it that

way, maybe it’s some type of solid material. But anyway, those

were, hopefully, two fairly straightforward

Snell’s law problems. In the next video, I’ll do a

slightly more involved one.

UberHaxorRobPost authorGreat as always!!!

thx alot

you are a good man

LAnonHubbardPost authorI paused the video at 2:01, got my TI-85 out and did the calculation. It was pretty funny (well, to me anyway) that the next step in the video was a TI-85 appearing on the screen working it out 🙂

xepIkzxxPost author@pysgodfach ..snell's law =]

xepIkzxxPost authorlovedddddddddd ur calculator..loll =P

thnk u so much Mr.Khan

Syed AliPost authorYOU ARE AMAZING

AT MPost authorWhere can I download that calculator? That is awesome!

jonrty007Post authorWhere'd you get that calculator? O_O

MrChin000Post authorThank you! But I have one question. In the second example another formula I am familiar with to find refractive index is sin i/sin r = n . Isn't the angle of incidence 30° and the angle of refraction is 40°? Therefore the refractive index of the unknown medium = sin 30°/sin 40° = 0.78?

Genna GPost authorYou are god.

Michl D.Post authorI wish you were my teacher 🙁 anyway tks!!

zain1612Post authorexcellent video

Javier PerezPost authoryou saved my life dude , thanks !

Nunchakus7Post authorlol super slow :)) 9:57

Catmail 555Post authoryour voice is so sexy.. just sayin'

owned2deathPost authorHey, I'm doing physics right now and I'm not that good at maths.. I was just wondering if you have a video that teaches how to solve for theta in that equation because I can get the equation but I don't know how to solve it. (sorry if it sounds stupid) :

Would anyone know what the topic I should practise in maths to get better at this would be?

Thanks heaps btw, you're video's are great!

Thanks

taylor watlingPost authorDude amazing vids… i have a test in two days and im set!

BCbonelessPost authorTexas Instruments website lets you download some of their calculators. The one Kahn uses looks like the TI-83. (Very handy for graphing on your PC.)

musiclover1453Post authorThank you for this video! =D

jonrty007Post authorThanks for the reply even if my comment was already a year old. :p

BOSSPost authorThank you

Abdulla AnaziPost authoris there a way to solve for the angle Theta without using the calculator

lyokofan212Post authori wonder if watching videos like this counts as studying?

ladymusicloverPost authorYou need a calculator to work it out.

nishan shahPost authoryou are the best teacher in the wold …

Niharika MathurPost authoryep, it definitely does if its going into your head!

MavrouPost authorU just saved me from failing my science!

NicolepuddingPost authorThank you soooooo much for this useful video, my hope of passing this physics exam rise again!!!

ca13Post authorYOUR CALCULATION IN THE SECOND EXAMPLE IS INCORRECT! the absolute refractive index is supposed to be 0.78 where sin 30 is divided by sin 40. you made a mistake and did it the other way around. the refractive index is equal to the sine of incident angle divided by the sine of refractive angle.

alexisundeadPost authorThank you SO much for making this video!! It was insanely helpful!

Nathanael SiahaanPost authorYOUR ARGUMENT IS INVALID! check your multiplcation and algebraic fractions again! it's absolutely true!

StuTTeraXPost authorTHAAAANKYOUUUUUUU <3

symphonicityPost authorCan anyone shed light on what the critical angle is? I am trying to solve a problem in which it gives a critical angle and asks me to find a refractive angle. Thank you.

Joshua PrestonPost authorTHANK YOU

makaveli thedonPost authorI understand where you are coming from. But you have to understand that when we are talking about the refractive index of a material we are saying that when light travels from air(or preferably a vacuum) into that material. So in essence, you are kinda using the 40° as the incident ray.

HeatProductionsPost authorSal, U made me understand the concept which i was trying to learn & understand since last 2 weeks xD TY MAN

Shrey MittalPost authori can't even use his calculator

Thomas DavisPost authorFor the second example I looked up what the material could be, and with an index of 1.29 the material was Fluorine refrigerant R-12. @Khan Academy

Goat ManPost authorthanks a lot 🙂 hahaha

Snicker SurpentinePost authoromg thank you dude u taught me the last 4 months of science in like a day of videos. teachers should use this for class

Felicia GrecoPost authorthank you so much!! I was ready to cry when I tried to understand snell's law and couldn't grasp it. now I no I wont fail that portion of my test tomorrow 😉 God bless!!

Shajeeah RamjaunPost authorthanks a million!! it all makes sense now! first time my teacher mentioned those it was as if he was speaking latin, now its so simple!

lavanyaPost authorthanks so much Sal. if I get good marks in my boards in phy. I'll give full credit to you.

A JPPost authorSo the general formula for it is nsin angle of inidence = sin beta 2

Quinn BullerPost authorI PASSED! ILY MAN

Tal AdivPost authorYour terrific analogy of car going from road to mud (or sand) really hit the spot for me.. Thanks!

I am convinced that all your blessed educational efforts have proven VERY fruitful the world over 🙂

a jPost authorthe air should be 1.0003 not 1.00029

Ruqi BibiPost authorTHANK YOUUUUUU LIFE SAVER

DareDog101Post authorI'm still not getting degrees

Tabasco 59Post authordo people only from texas us Tis or do others states use them too! im interested to know.

sumit kumarPost authorMy new PHYSICS SOLVING APP.More then 150+ formulas,Solves for any variable you want,Covers up all physics.download now.https://play.google.com/store/apps/details?id=com.physics.lenovo.myapplication

i want milk.Post authorSo finding the refractive index is basically n= sin r/sin i? I thought finding the refractive index is n= sin i/sin r?

Hunter EgesdalPost authorYou just saved my physics final. I thank you kind sir.

Dylan HerreraPost authorTy so much

Aubrey AlagosPost authorI am a biology teacher, but I am asked to teach a general science course including this topic. Thanks so much. 🙂 Teacher helping teachers.

David disantoPost authoryour a beauty

pranav bhaskarPost authorThe refractive index for

Dichlorodifluoromethanerefrigerant R-12is 1.29Summer KroeplinPost authorThank you so much

raji samusideenPost authorThanks man my physics exam is tomorrow and am sure am gonna pass