Physics 102: Lecture 18 Snell’s Law, Total Internal …...Total Internal Reflection only works if n outside < n inside At each contact w/ the glass air interface, if the light hits

Physics 102: Lecture 18, Slide 1

Snell’s Law, Total Internal Reflection, Brewster’s Angle,

Dispersion, Lenses

Physics 102: Lecture 18


Summary of today’s lecture

• Examples of refraction– 1) Total internal reflection– 2) Brewster’s angle– 3) Dispersion (rainbows)– 4) Lenses


Demo: Snell’s Law

n2

n1 > n2

When light travels from one medium to another the speed changes v=c/n, but the frequency is constant. So the light bends:

n1 sin(θ1)= n2 sin(θ2)

θ1

θ2

θr

incidentreflected

refracted

n1 > n2 ⇒ θ2 > θ1

Light bent away from normal as it goes in medium with lower n


1) Total Internal Reflection

normal

n2

n1 > n2

Snell’s Law: n1 sin(θ1)= n2 sin(θ2)(n1 > n2 ⇒ θ2 > θ1 )

θ1 = sin-1(n2/n1) then θ2 = 90

Light incident at a larger angle will only have reflection (θi = θr)

“critical angle”

For water/air:n1=1.33, n2=1θ1 = sin-1(n2/n1)

= 48.80

θ1

θ2

θi > θcθr θc


Fiber Optics

Telecommunications

Arthoscopy

Laser surgery

Total Internal Reflection only works if noutside < ninside

At each contact w/ the glass air interface, if the light hits at greater than the critical angle, it undergoes total internal reflection and stays in the fiber.

ninside

noutside


Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection?

1) Yes 2) No

Preflight 18.1


ACT: Refraction• As we pour more water into bucket, what

will happen to the number of people who can see the ball?

1) Increase 2) Same 3) Decrease


2) Brewster’s angle

When angle between reflectedbeam and refracted beam is exactly 90 degrees, reflected beam is 100% horizontally polarized !

Reflected light is usually unpolarized (mixture of horizontally and vertically polarized). But…

tan θB =

n2

n1

n1 sin θB = n2 sin (90-θB)

n1 sin θB = n2 cos (θB)

horiz. and vert. polarized

θB θB

90º – θB

90º

horiz. polarized only!n1

n2


ACT: Brewster’s AngleWhen a polarizer is placed between the light source and the surface with transmission axis aligned as shown, the intensity of the reflected light:

(1) Increases (2) Unchanged (3) Decreases

T.A.


Polarizing sunglasses are often considered to be better than tinted glasses because they…

Preflight 18.3, 18.4

• block more light• are safer for your eyes• block more glare• are cheaper

Polarizing sunglasses (when worn by someone standing up) work by absorbing light polarized in which direction?

• horizontal• vertical


3) Dispersion

Prism Blue light gets deflected more

nblue > nred

The index of refraction n depends on color!In glass: nblue = 1.53 nred = 1.52

White light

θblue < θred

θred

θi

θblue


Skier sees blue coming up from the bottom (1), and red coming down from the top (2) of the rainbow.

Rainbow: Preflight 18.5

Which is red?

Which is blue?

Blue light is deflected more!


LIKE SO! In second rainbow pattern is reversed


4) Lenses

Focal point determined by geometry and Snell’s Law: n1 sin(θ1) = n2 sin(θ2)

Converging lens:– Rays parallel to P.A. converge on focal point

Diverging lens:– Rays parallel to P.A. diverge as if emerging from focal point behind lens

Larger n2/n1 = more bending, shorter focal length.Smaller n2/n1 = less bending, longer focal length.n1 = n2 => No Bending, f = infinity

F

θ1θ2

θ1 θ2

“Plano-convex”

“Plano-concave”

P.A.

F P.A.


Converging & Diverging Lenses

Converging lens:– Rays parallel to P.A. converge on focal point

Diverging lens:– Rays parallel to P.A. diverge as if emerging from focal point behind lens

“Plano-convex”

“Plano-concave”

Converging = fat in the middle

Diverging = thin in the middle “Double concave”

“Double convex”

= =

= =

“Convex-concave”

“Concave-convex”


1) Rays parallel to principal axis pass through focal point.2) Rays through center of lens are not refracted.

3) Rays through F emerge parallel to principal axis.

Converging Lens Principal Rays

F

F

Object

P.A.

Image is: real, inverted and enlarged (in this case).

Image

Key assumptions:• monochromatic light incident on a thin lens.• rays are all “near” the principal axis.


Converging LensAll rays parallel to principal axis pass through focal point F. Double Convex

P.A.

nlens > noutside

F

• At F

• Inside F

• Outside F

P.A.

F

Preflight 18.6A beacon in a lighthouse produces a parallel beam of light. The beacon consists of a bulb and a converging lens. Where should the bulb be placed?


3 Cases for Converging Lenses

Object

Image

This could be used in a camera. Big object on small film

InvertedReducedReal

Past 2F

Image

Object

This could be used as a projector. Small slide on big screen

InvertedEnlargedReal

BetweenF & 2F

Image Object

This is a magnifying glass

UprightEnlargedVirtual

Inside F

http://www.lightlink.com/sergey/java/java/clens/index.html


ACT: Converging LensWhich way should you move object so image

is real and diminished?

(1) Closer to lens(2) Further from lens(3) Converging lens can’t create real

diminished image.

F

F

Object

P.A.


1) Rays parallel to principal axis pass through focal point.

2) Rays through center of lens are not refracted.

3) Rays toward F emerge parallel to principal axis.

Diverging Lens Principal Rays

F

F

Object

P.A.

Only 1 case for diverging lens:

Image is always virtual, upright, and reduced.

Image


Which way should you move object so image is real?

1) Closer to lens2) Further from lens3) Diverging lens can’t create real image.

ACT: Diverging Lenses

DemoF

F

Object

P.A.

http://www.lightlink.com/sergey/java/java/dlens/index.html

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Physics 102: Lecture 18 Snell’s Law, Total Internal …...Total Internal Reflection only works if n outside < n inside At each contact w/ the glass air interface, if the light hits