Reflection and Reflection and RefractionRefraction

ReflectionReflection Reflection occurs when light bounces Reflection occurs when light bounces

off a surface.off a surface. There are two types of reflectionThere are two types of reflection

– Specular reflectionSpecular reflection Off a shiny surfaceOff a shiny surface

– Diffuse reflectionDiffuse reflection Off a rough surfaceOff a rough surface

Ray tracingRay tracing Ray tracing is a method of Ray tracing is a method of

constructing an image using the constructing an image using the model of light as a ray.model of light as a ray.

We use ray tracing to construct We use ray tracing to construct optical images produced by mirrors optical images produced by mirrors and lenses.and lenses.

Ray tracing lets us describe what Ray tracing lets us describe what happens to the light as it interacts happens to the light as it interacts with a mediumwith a medium

Types of mirrorsTypes of mirrors Plane mirrorsPlane mirrors

Spherical mirrorsSpherical mirrors

Law of ReflectionLaw of Reflection The angle of incidence of reflected The angle of incidence of reflected

light equals the angle of reflection.light equals the angle of reflection. θθRR = = θθII

Note that angles are measured Note that angles are measured relative to a normal to the mirror relative to a normal to the mirror surface.surface.

Optical imagesOptical images NatureNature

– real (converging rays)real (converging rays)– virtual (diverging rays)virtual (diverging rays)

OrientationOrientation– uprightupright– invertedinverted

SizeSize– truetrue– enlargedenlarged– reducedreduced

Ray tracing: plane mirrorRay tracing: plane mirror

Construct the image using two rays.Construct the image using two rays.

5 cmobject

-5 cmimage

Plusside

Minusside

Upright (virtual)Same size

Reflected raysAre diverging

Extend reflectedrays behind mirror

The focal point is where the rays intersect!

Going from concave to convex the focal point stays on the concave side of the mirror!

Rays parallel to the principal axisall pass through the focus for aSpherical concave mirror.

The focal length is always ½ of the radius!

r

f

r is the radius of curvature

C is the center of the sphere

F is the focal length of the mirror

θ

Law of Reflection still Law of Reflection still works even on a curved works even on a curved surface (just like a rough surface (just like a rough surface)surface)

θθ

Ray tracing: spherical concave mirror The three “principal rays” to construct an

image for a spherical concave mirror are– the p-ray, which travels parallel to the

principal axis, then reflects through focus.– the f-ray, which travels through focus, then

reflects back parallel to the principal axis.– the c-ray, which travels through center, then

reflects back through center. You must draw two of the three You must draw two of the three

principal rays to construct an image.principal rays to construct an image.

Construct the image for an object located outside the center of curvature. It is only necessary to draw 2 of the threeIt is only necessary to draw 2 of the three principal rays!principal rays!

p ray p ray

c rayc ray F rayF ray

Real image, inverted image, reduced image

Construct the image for an object located at the center of curvature. Name the image.Name the image.

p ray p ray

F rayF ray

Real image, inverted image, true image

p rayp ray

f rayf ray

c rayc ray

Real, Inverted, Enlarged Image

Construct the image for an object located at the focus.

p ray p ray

c rayc ray

No image

Construct the image for an object located inside the focus. Name the image.

p ray p ray

c rayc ray

Virtual, Upright, Enlarged Image

f rayf ray

Object is at “C”

Object and image meet! (As object moves toward mirror, image moves away)

(remember to right-click anywhere to pause)

Object is between “C” and “F”

Object is between “F” and mirror

Side-by-side comparison (remember to right-click

anywhere to pause)

What’s the difference between a REAL and a VIRTUAL image?

What’s the difference between a REAL and a VIRTUAL image?

A REAL image is on the SAME SIDE of the mirror as the object making the

image.

The Mirage demo creates a real image. Usually you need to project the REAL image onto a screen so you can see it.

Like Alice in Wonderland objects not in the mirror (in Wonderland) are REAL or in the REAL world.

What’s the difference between a REAL and a VIRTUAL image?

A VIRTUAL image we trace the rays back to a point where the rays appear to diverge.

The image appears to be on the opposite side of the reflective surfac

Mirror equationsMirror equations

1/s1/sii + 1/s + 1/soo = 1/f = 1/f– ssii: image distance: image distance– ssoo: object distance: object distance– f: focal lengthf: focal length

M = hM = hii/h/hoo = -s = -sii/s/soo

– hhii: image height: image height– hhoo: object height: object height– M: magnificationM: magnification

Sign conventionsSign conventions Focal length (f)Focal length (f)

– Positive for CONCAVE mirrorsPositive for CONCAVE mirrors– Negative for CONVEX mirrorsNegative for CONVEX mirrors

Magnification (M)Magnification (M)– Positive for UPRIGHT imagesPositive for UPRIGHT images– Negative for INVERTED imagesNegative for INVERTED images– ENLARGED when M > 1ENLARGED when M > 1– REDUCED when M < 1REDUCED when M < 1

Image DistanceImage Distance– ssii is POSITIVE for real images is POSITIVE for real images– ssii is NEGATIVE for virtual images is NEGATIVE for virtual images

RefractionRefraction

The bending of light raysThe bending of light rays

Refraction FormulasRefraction Formulas

Index of RefractionIndex of Refraction

v

cn

n = index of refractionv = speed of light in materialc = speed of light in a vacuum

FormulasFormulas

Snell’s LawSnell’s Law

ni sin i = nr sin r

 i = angle of incidenceni = index of refraction for incident mediumr = angle of refractionnr = index of refraction for refracting medium

The speed of light in plastic is 2.00 x 108 m/s. What is the index of refraction of plastic?

 n = ?v = 2.00 x 108m/sc = 3.00 x 108 m/sn = 3.00 x 108 m/s / 2.00 x 108m/s

n = 1.5 

Sample ProblemSample Problem

Notes – Refraction/Snell’s Law When light passes from one medium into another,o   part of the incident light is reflected at the boundary and

o   the remainder passes into the new medium-if the ray enters the new medium at an angle (other than perpendicular), the ray bends as it enters.

  A ray of light traveling through air is incident upon a sheet of crown glass at an angle of 30o. What is the angle of refraction? 

ni sin i = nr sin r

ni = 1.00

i = 30o

nr = 1.52 (1.00)(sin 30o) = (1.52)(sin r)

r = ?? 0.500 = sin r

1.52r = 19.2o

Sample ProblemSample Problem

When light passes from one material into a second material where the index of refraction is less (say, from water into air) light bends away from the normal. 

At a particular incident angle, the angle of refraction will be 90o, and the refracted ray will skim the surface. The angle of incidence at which this occurs is called the critical angle.

Critical AngleCritical Angle

Sample ProblemSample Problem

Find the critical angle for diamond.Find the critical angle for diamond.  

nnii = 2.42 (diamond) = 2.42 (diamond)

nni i sin sin ii = n = nrr sin sin rr

cc = ? = ?

nnrr = 1.00 (vacuum) = 1.00 (vacuum)

rr = 90 = 90oo

(2.42)(sin (2.42)(sin cc) = (1.00)(sin 90) = (1.00)(sin 90oo) )

cc = 24.4 = 24.4oo

incident ray

Normal (90o)

θi θr

θi θr

The arrangement shown at the left is thicker in the middle and converges the light. The arrangement at the right, however, is thinner in the middle than at the edges; it diverges light 

30-2

Converging, because the rays intersect (converge)

30-2

Diverging, because the rays move away from each other (diverge)

Convex Lenses:

The lens below is a convex lens – also known as a converging lens.

The lens below is a concave lens, also known as a diverging lens.

 

The thin lens equations are the same as the mirror equations.

 

However, there are different sign conventions that go along with using the equation for lenses.

The Thin Lens Equation

 

io ddf

111

o

i

o

i

d

d

h

hM

For converging lensesFor converging lenses

f is positivef is positive ddoo is positive is positive ddii is positive for real images an is positive for real images an

negative for virtual imagesnegative for virtual images M is negative for real images and M is negative for real images and

positive for virtual imagespositive for virtual images hhii is negative for real images and is negative for real images and

positive for virtual imagespositive for virtual images

For diverging lensesFor diverging lenses

f is negativef is negative ddoo is positive is positive

ddii is negative is negative M is positive and < 1M is positive and < 1 hhii is positive and < h is positive and < hoo