Light Ray, Light Ray

A Cruise Through the Wonderful World of Reflection and Refraction

(aka Geometric optics)

No Light, No Sight

Presentation Text ©2001 Philip M. Dauber

What is Light?

• Electromagnetic Radiation with wavelength

(visible) 400 to 700 nm (nanometers) or 4x10-7 to 7x10-7 meters

• Travels in straight lines

• Bounces (reflects) off certain materials

• Refracts (bends) in transparent materials

• Travels at c = 3 x 108 m/sec (in vacuum)

Reflection

• Light bounces off objects

• Consider “rays” – light moving in straight line

• Law of reflection: angle of incidence = angle of reflection

Law of Reflection

Law of Reflection i = r

• I - incident ray

• R - reflected ray

• N – normal

• Theta-I is angle of

incidence

• Theta –R is angle of

reflection

Types of Reflection

How Plane Mirror Forms Image

Image From Plane Mirror

• Virtual

• Behind mirror

• Right side up(upright)

• Left-right reversed

• Located equal

Distance behind mirror

• Same size as object

Distance RelationshipImage is as far behind mirror as object is in

front

How Curved Mirror Forms Real Images

How Law of Reflection Leads to Images from Spherical Mirror

• C is center of

curvature

• F is focal point

• Real image will

be located on same side

of mirror as object

Rules of Reflection – Two “Special” Rays

• An incident ray parallel to principal axis will pass through the focal point after reflection.

• An incident ray passing through the focal point will leave mirror parallel to principal axis

What’s So “Special?” About Special Rays?

• Its easy to predict where they will go

• Use Law of Reflection

Ray Diagram – Object Beyond C = 2f

• Real image

• Inverted

• Smaller than object

• Note use of two

“special” rays

• What is another?

Ray Diagram – Object at C = 2f or between f and 2f

• Image inverted• Located at 2f • Same size as object

• Image inverted• Further than 2f• Larger than object

Object at 2f

Object Between f and 2f

Object Closer to Mirror Than f “Shaving Mirror” Case

• Image virtual

• Behind mirror

• Upright

• Larger than object

Object at f

• Must use different ray (goes to intersection of principal axis and mirror)

• No image formed

Object Closer to Mirror Than F

Mirror Equation

• f is positive for concave mirror

Question: Where will image formed by a lens with 20 cm focal length be if object is placed 30 cm from mirror?

How Big is The Image?

• M is magnification

• - sign means image is inverted

Question: If the object in the question on previous slide is 2 cm high, how high is image?

Convex (Diverging) Mirrors

• f is negative

• Light rays spread,

not focused; images virtual

• 7-11 mirror foils

thieves

Ray Diagram for Convex Mirror

• One ray parallel to p.a.

• Second ray heads for

focus behind mirror

• Diverging rays must be

extended behind mirror

(dotted lines)

• Image virtual, upright, smaller

Why Are Some Rearview Mirrors Convex?

Problem

• A 1.6 m tall thief stands 10m away from a 7-11 mirror with 2m (negative) focal length.

Where is the image and how tall is it?• Use

• Note: negative di means image behind mirror

Index of Refraction

• Light slows down in transparent materials other than vacuum(like car slows in sand)

• v = c/n velocity of light in medium

• n is called index of refraction

• n = about 1.5 for glass

• n = 1.33 for water

Index of Refraction

• Ratio of speed of light in vacuum to speed of light in material

• n = c/v = 3.0 x 108 m/s/v• n always greater than one

Refraction: How Much Does It Bend?

• Angle of incidence i

• Angle of refraction r

• Snell’s Law:

ni sin i = nr sin r

Helpful Analogy:The Band of Sand

• What happens when the car drives into the sand?

highway sand

Which way does the car turn?

Toward and Away from Normal

• When light enters a more dense (greater n) medium, it bends toward the normal

• When light enters a less dense (smaller n) medium, it bends away from the normal

Mysteries?

• Why do a person’s legs appear shorter when they are standing in water?

• Why Does A Glass Rod Disappear in Mineral Oil?

Problem

• Light strikes a flat piece of glass(n = 1.5) at 60 degrees to the normal. What is the angle of the light in the glass?

i = 60o

r

Solution

• ni sin i = nr sin r

• ni = 1 nr = 1.5

sin r = 1.00/1.50 sin i = 0.577

r = 35.2o

Critical Angle• Light ray leaves more dense medium

• Angle of refraction approaches 900

• Past critical angle there is no refracted ray

Critical AngleThe angle of incidence past which there is no

refracted ray

• ni sin i = nr sin r

• sin c = nr/ni sin900 = nr/ni

• If ray emerges into air• sin c = 1/ni

c

Example

• What is the critical angle for light rays leaving a swimming pool? What does the world look like to a swimmer at the bottom of the pool?

Sin c = 1.00/1.33 = 0.750

c = 490

Swimmer sees outside world compressed into a circle whose edge makes a 49 degree angle to the vertical

Total Internal Reflection

Applications of TIR

• Prisms in Binoculars, Periscopes

Dispersion• Separation of white light into spectrum of

wavelengths (colors)

Why Dispersion Occurs

• Index of refraction, n, depends on wavelength

• Typically n decreases as increases

• Exit angle from prism depends on

White light

Forming a Rainbow

Fiber Optics

• Fiber Optic Amplifier Module

                                                                                                 

Spy under door optics

                                                           

endoscopePhotos courtesy JDS Uniphase Inc.

Lenses

• Lenses can focus or diverge light

• Act like tiny prisms

Thin Lens

• Convex lenses have two focal points

Focal Length of Lens

• That distance, f, from lens at which parallel rays are brought to a point

• Power of a lens:

P = 1/f

• Unit is “diopter” (m-1)

• Used by optometrists

Focal point

Three Special, Predictable Rays

• Avoid application of Snell’s Law

• Parallel to principal axis, exiting rays goes through far focus

• Through near side focus; exiting ray parallel

• Through center of lens (no refraction)

Object Distance Greater than 2f

• Image real

• Inverted

• Smaller

• Opposite side

from object

• Like camera

Object at 2f or between f and 2f

• Image same size, real• At 2f

• Image larger, real• Greater than 2f• Like projector

Diverging Lens – Does NOT focus

• Image virtual

• Upright

• Smaller

• Same side

as object

• Closer than f

Thin Lens Equation

• F positive for converging lens, negative for diverging lens

• di positive for real images, negative for virtual images (same side)

Magnification

• Relates image and object height to image and object distance

Solving Lens Problems

• Read and re-read problem• Draw ray diagram with 2 or 3 special rays• Solve lens and magnification equations for

unknowns• Follow sign conventions including

– f positive for converging lenses– f negative for diverging lenses– di negative on same side of lens as object

Lens Problem

• A fly one cm tall is 30 cm from a lens with a focal length of 20cm. Where is the (real) image of the fly located and how tall is it?

1/di = 1/f – 1/d0 = 1/20 – 1/30 = 3/60 – 2/60 = 1/60

di = 60 cm on other side of lens from fly

hi = -h0 di/d0 = -2cm

- sign means image inverted

Object Inside of f – Magnifying Glass

• Image virtual

• Upright

• Same side as object,

behind object

• larger

Problem

• An object is placed 10 cm from a 15cm focal length converging lens. Where is the image?

1/di = 1/f – 1/d0 = 1/15 – 1/10 = -1/30

di = -30 cm

- sign means image is virtual and n same side of lens as object

Object at f

• No image formed

Diverging Lens Problems

• Remember, f is negative

• di will also be negative

Problem

• Where must a small insect be placed if a 25 cm diverging lens is to form a virtual image 20 cm in front of the lens?

1/d0 = 1/f – 1/di = -1/25 + 1/20 =

(-4+5)/100 = 1/100

d0 = 100 cm in front of lens

Combinations of Lenses and Lenses with Mirrors

• The image produced by the first element becomes the object of the second

• Two converging lenses with focal lengths 20.0 and 25.0 cm respectively are placed 80.0 cm apart. An object is placed 60 cm in front of the first lens. Where is the image?

Lenses and Mirrors

• Sketch a ray diagram of a set up in which a mirror and a lens work together

• Find out how an astronomical telescope works– Refracting– Reflecting

• Find out how a simple compound (two lens) microscope works

Acknowledgements

• Graphics and animation courtesy of Tom Henderson, Glenbrook South High School, Illinois

• Photos of fiber optic components courtesy of JDS Uniphase, Inc