Department of Physics and Applied Physics PHYS.1440 Lecture 23 A.Danylov Lecture 23 Chapter 23 Ray Optics Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII Physics II
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Let’s finish talking about
a diffraction grating
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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?
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Ray Optics
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Ray Optics
Wave Optics
∼ (object size)
Ray Optics
≪ (object size)
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Reflection
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Refraction
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Indices of RefractionThe index of refraction is used to describe optical properties of a transparent medium.
Speed of light in a medium
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Total internal reflection
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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:
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
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.
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
What you should readChapter 23 (Knight)
Sections 23.1 23.2 23.3
Department of Physics and Applied PhysicsPHYS.1440 Lecture 23 A.Danylov
Thank youSee you on Tuesday