L24 Ch23 Rays Snell Law - faculty.uml.edu

Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov

Lecture 23

Chapter 23

Ray Optics

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Physics II


Let’s finish talking about

a diffraction grating


Diffraction Grating

Thus, we can replace the double slit with an opaque screen that has N closely spaced slits.

A large number of equally spaced parallel slits is called a diffraction grating.

Δ

2 cos

Number of slits

Spacing between bright spots:

Intensity of bright spots:

We saw in the demo that the spacing between bright spots is inconveniently small ( mm), but we can increase the spacing by reducing d

We saw in the demo that the intensity of the bright spots is not bright enough, but we can increase brightness by increasing number of slits (N)

Let’s improve (more convenient to use) results of a double-slit system. How?


The Diffraction Grating

When illuminated from one side, each of these slits becomes the source of a light wave that diffracts, or spreads out, behind the slit. A practical grating will have hundreds or even thousands of slits.

The figure shows a diffraction grating in which N slits are equally spaced a distance d apart.

Physics and math are the same as for a double-slit experiment

Bright fringes will occur at angles m.

It’s easier to measure distances on the screen than angles: θ → y0,1,2,

sin ,

∙ ,

However, these angles are NOT SMALL AND the equations CANNOT BE SIMPLIFIED like we did for the 2slit experiment.Thus, using these two equations we can find positions of the bright spots.The integer m is called the order of the diffraction.


Diffraction grating intensity

Now with N slits, the wave amplitude at the points of constructive interference is Na.

Because intensity depends on the square of the amplitude, the intensities of the bright fringes are:

Not only do the fringes get brighter as N increases, they also get narrower.

The bright spots are no longer equally spaced.


Measuring wavelength emitted by a diode laser (with a demonstration)

Light from a diode laser passes through a diffraction grating having 300 slits per millimeter. The interference pattern is viewed on a wall 2.5 m behind the grating.

Calculate the wavelength of the laser.


Ray Optics


Ray Optics

Wave Optics

∼ (object size)

Ray Optics

≪ (object size)


The Ray Model of Light

Wave fronts

Ray

Ray

Ray

Ray

Now, we will model light with rays, straight lines ┴ to wave fronts.

This model is valid as long as an object is very large compared to the wavelength.

Let us define a light ray as a line in the direction along which light energy is flowing.

Any narrow beam of light, such as a laser beam, is actually a bundle of many parallel light rays.


Types of objects

Ray

Self-luminous object (active)It emits light

Reflective object (passive)It reflects light

Objects can be either self-luminous, such as the sun, flames, and lightbulbs, or reflective.

Most objects are reflective.


How Rays interact with media

Light interacts with matter in four different ways:At an interface between two materials, light can be either reflected or refracted.Within a material, light can be either scattered or absorbed.

Medium 1 Medium 2

Reflection

Refraction


Reflection


Two types of reflections

Incident ray Reflected ray

Specular Reflection(from a smooth surface)

‐ angle of incidence‐ angle of reflection

Law of reflection: 1. Incident and reflected rays and a normal line

are in the same plane2. Angle of incident equals to angle of reflection

Diffuse Reflection(from a rough surface)

Incident ray

Reflected

For a “rough” surface, the law of reflection is obeyed at each point but the irregularities of the surface cause the reflected rays to leave in many random directions.

It is how you see this slide, the wall, your hand, your friend, and so on.

Most objects are seen by virtue of their reflected light.


Image in a plane mirror I Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P, the same distance behind the mirror

as P is in front of the mirror. That is, s = s.

ssmirror

Cat vs Mirror


Image in a plane mirror II

Two point sources of light illuminate a narrow vertical aperture in a dark screen. What do you see on the viewing screen?

ConcepTest Ray Optics

scre

en


Refraction


Refraction

Two things happen when a light ray is incident on a smooth boundary between two transparent materials:

1. Part of the light reflects from the boundary, obeying the law of reflection.

2. Part of the light continues into the second medium. The transmission of light from one medium to another, but with a change in direction, is called refraction.

Refracted ray


Indices of RefractionThe index of refraction is used to describe optical properties of a transparent medium.

Speed of light in a medium


RefractionConsider a smooth boundary between two transparent materials

Incident ray Reflected rayangle of incidence

angle of refraction

Normal

Medium 1Medium 2

Refracted ray

Assume n2 > n1The ray has a kink

at the boundary


Refraction When a ray is transmitted into a material

with a higher index of refraction, it bends toward the normal.

n2 > n1 n2 < n1It bends away from the normalIt bends toward the normal

When a ray is transmitted into a material with a lower index of refraction, it bends away from the normal.

A laser beam passing from medium 1 to medium 2 is refracted as shown. Which is true?

ConcepTest RefractionA. n1 < n2.B. n1 > n2.C. There’s not enough information to

compare n1 and n2.

n2 < n1

It bends away from the normal

The end of the class


Total internal reflection


Total Internal Reflection

The refracted light vanishes at the critical angle and the reflection becomes 100% for any angle 1 > c.

Incident ray Reflected ray

angle of incidence

angle of refraction

Normal

airglass

Refracted ray

n2 < n1n1

=900

<

When a ray crosses a boundary into a material with a lower index of refraction, it bends away from the normal.

As the angle 1 increases, the refraction angle 2 approaches 90, and the fraction of the light energy transmitted decreases while the fraction reflected increases.

The critical angle of incidence occurs when 2 = 90:


Critical angle (TIR)angle of refraction

Normal

airglass

Refracted ray

n1

=900n2 < n1

Critical angle (incident angle)

=900 Angle of refraction, so

sin sin 901

sinCritical angle

Total Internal Reflection


Fiber Optics The most important modern application of total internal reflection

(TIR) is optical fibers. Light rays enter the glass fiber, then impinge on the inside wall of

the glass at an angle above the critical angle, so they undergo TIR and remain inside the glass.

The light continues to “bounce” its way down the tube as if it were inside a pipe.



What you should readChapter 23 (Knight)

Sections 23.1 23.2 23.3


Thank youSee you on Tuesday

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L24 Ch23 Rays Snell Law - faculty.uml.edu