Physics 1230: Light and Color Exam 1 is finished, Avg: 84 +/- 10.5 Solutions on the web and scores on CULearn. HW4: Due Thursday, 5PM Lecture 6: Reflection, mirror images, and refraction. Reading: Chapter 2, pgs. 29-68 1
Chapter 2 Geometrical Optics Geometrical optics is the theory of RAYS (straight lines) and how they reflect and refract (bend). Lots of similarity to GEOMETRY of lines and triangles. Main Topics We are here 1. Shadows 2. Reflection 3. Refraction 4. Dispersion 2
Chapter 2 Geometrical Optics We are here 1. Shadows 2. Reflection a) Specular or diffuse b) Equal angle rule c) images, ray tracing 3. Refraction 4. Dispersion a. Point source or diffuse source b. Umbra and penumbra c. How tall is my shadow? d. Pinhole camera 3
Specular or diffuse? Diffuse reflection (paper) Specular reflection (mirror) Diffuse transmission (wax paper) 4
Equal angle rule q i = angle of incidence q r = angle of reflection q i = q r is specular reflection Incident Ray q i q r Reflected Ray Normal A normal is a line perpendicular to the surface. 5
Materials like metals with many mobile electrons can cancel out the light wave field in the forward direction so there is no transmission but only reflection at certain wavelengths. Metals reflect all waves below a certain frequency the plasma frequency - which varies from metal to metal Silver is particularly interesting because it reflects light waves at all visible frequencies Its plasma frequency is at the top of the violet so it reflects all of the wavelengths below and appears whitish Gold and copper have a yellowishbrownish color because they reflect greens, yellows and reds but not blues or violets Red and green make yellow Plasma frequency of silver Plasma frequency of gold Plasma frequency of copper
What is a mirror? Since silver is such a good reflector a coating of silver on glass makes a good (common) mirror. If the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50% This is called a half-silvered mirror A half-silvered mirror used with proper lighting can show objects on one side or the other of the mirror
Law of specular reflection of a ray from a mirror One of many rays from a light bulb hits Alex's chin. The ray from the light bulb is diffusely reflected off his chin. We show one of the many rays coming off his chin hitting a mirror. This is called an incident ray The incident ray undergoes specular reflection off the mirror Note the reflected ray Draw the normal to the mirror The angle of incidence = the angle of reflection This angle Normal = this angle The normal to the mirror is an imaginary line drawn perpendicular to it from where the incident ray hits the mirror
How is an image produced in a mirror? Part 1: Ray-tracing To find out how Bob "sees" Alex by looking in the mirror we trace rays which obey the law of reflection Consider an incident ray from Alex's chin which reflects according to the law of reflection at a specific point on the mirror and goes into Bob's eye. Note - it is not easy to construct this ray! You cannot arbitrarly choose a point on the mirror and expect that the law of reflection will be satisfied Bob will see only this reflected ray from Alex's chin. Other refelected rays from Alex's chin will miss his eye (see right) A ray from Alex's hair will reflect at one point on the mirror into Bob's eye (and satisfies the law of reflection) Alex Bob looks at Alex's image
How is an image produced in a mirror? Part 2: The psychology of ray interpretation To find the image of Alex we must learn how Bob s eye (and our eyes) interpret rays Bob cannot directly know whether the rays entering his eyes have been reflected or not! We interpret all rays coming into our eye as traveling from a fictitious image in a straight line to our eye even if they are reflected rays! To find the virtual (fictitious) image of Alex s chin we extend each reflected ray backwards in a straight line to where there are no real rays Extend the ray reflected into Bob's eye from Alex's chin backward behind the mirror. Extend the ray reflected towards Bob's chest (why?) from Alex's chin backward (dashed line) behind the mirror. The image of Alex's chin will be behind the mirror at the intersection of the two backwardextended reflected rays. Note all reflected rays from his chin intersect at the same image pt. when extended backwards Alex Bob looks at Alex's image To find the location of his hair in the virtual image we extend any reflected ray from his hair backwards
How is an image produced in a mirror? Part 3: The meaning of a virtual image If we trace rays for every ray from every part of Alex which reflects in the mirror we get a virtual image of the real Alex behind the mirror. It is virtual because there is no light energy there, no real rays reach it, and it cannot be seen by putting a screen at its position!! When all of the reflected rays from Alex's chin are traced backwards they all appear to come from the virtual image of Alex s chin Hence Alex's image is always in the same place regardless of where Bob looks The image chin is behind the mirror by a distance = to the distance the real chin is in front of the mirror This is true for all parts of Alex's image Alex's virtual image is the same size as the real Alex Alex's image is further away from Bob than the real Alex Alex Virtual image of Alex is behind mirror Bob looks at Alex's image Bob sees Alex's image in the same place when he moves his head
Image in a mirror 1. If a point on the object is distance X in front of the mirror, the same point in the image appears to be distance X in back of the mirror, or X object = X image. 2. The image point is on the normal (extended) from the object to the mirror. normal extended X object X image 12
Ray tracing: Draw the image, then the rays First: draw rays from image to eyes Viewed from the side. X object X image 13
Ray tracing: Draw the image, then the rays First: draw rays from image to eyes Second: draw rays from mirror to object X object X image q i = q r happens automatically using this method. Demo on board 14
Right side up image? The top ray goes to the top of the bottle. It is right side up. X object X image q i = q r happens automatically using this method. 15
Right side up image? The top ray goes to the bottom of the bottle. It is upside down. X object Extension (to do this drawing, the mirror must be extended) X image q i = q r happens automatically using this method. 16
Bottle on its side Viewed from the side. (to do this drawing, the mirror must be extended) q i = q r happens automatically using this method. 17
For simple (flat) mirrors the image location is therefore predictable without knowing where the observer's eye is and without ray-tracing
A few words about virtual images Here is the real Alex Here are some (diffusely reflected) diverging rays coming off his nose They can be seen by eyes at various locations We only know his nose is there because our eyes receive the rays Therefore, we would see an image (virtual) of Alex if those rays reached our eyes even when he wasn't there. s can provide those rays! The (imaginary) extension of (reflected) rays behind the mirror look just like the real rays from the real Alex (incident rays not shown)
The image of the bottle in the lower mirror is: A) Inverted B) Not inverted C) Something else Periscope mirror Original OBJECT mirror 20
Periscope? The first IMAGE extension Original OBJECT 21
Periscope? extension The second IMAGE 22
The image of the bottle in the lower mirror is: A) Inverted B) Not inverted C) Something else Periscope? 23
Multiple mirrors - a virtual image can act as a real object and have its own virtual image Question: Where are the images of Alex in the 2 mirrors? a) At A only b) At B only c) At A and B only d) At C only e) At A, B and C Alex B The virtual image at A acts as an object to produce the virtual image of C. It acts as an intermediate image. More precisely it is the red rays which reflect as green rays. A C
AR Is the writing reversed? (Two mirrors, viewed from above) A) YES B) NO 25
AR Is the writing reversed? ЯA 26
AR Is the writing reversed? AR extension ЯA 27
AR Is the writing reversed? AR A) YES B) NO ЯA 28
Lec. 6: Ch. 2 - Geometrical Optics We are here 1. Shadows 2. Reflection 3. Refraction 4. Dispersion 29
Refraction 1. Index of refraction: n = c / v 2. Ray in water is closer to the normal 3. Total internal reflection 4. Mirages 30
No. Reflection of waves occurs where the medium of propagation changes abruptly Part of the wave can be transmitted into the second medium while part is reflected back You can hear someone from outside the pool when you are underwater because sound waves are transmitted from the air through the water (with different speed in each). When light waves are incident on a glass slab they are mostly transmitted but partly reflected (about 4%)! Glass slab Is the speed of light in the glass slab the same as in the free space???
How can reflection require that the speed of the wave changes? We thought the speed of light was always c = 3 x 10 8 m/s! The speed of an electromagnetic (EM) wave is constant (for every wavelength) in empty space! The speed of light is slower than c in glass, water and other transparent media (Einstein showed that light can never travel faster than c) The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction n = 1.5 for glass n = 1.3 for water n = 1.5 for vegetable oil Light is reflected and transmitted at a boundary because When a light wave travels in a medium the electric field of the light jiggles the electrons in the medium. This produces new electric fields which can cancel or add to the original light wave both in the forward and backward directions These are the transmitted and reflected light waves
Refractive indices of different materials Material Refractive Index Air 1.0008 Water 1.330 Glass 1.5 Diamond 2.417 Ruby 1.760 Oil 1.5 Can we see a glass rod immersed into the oil with the same refractive index? A. Yes B. No Demo