reflection and refraction of light

Transcription

1 physics course exercises Liceo Scientifico Belfiore - Mantova reflection and refraction of light in accordo con il Ministero dell Istruzione, Università, Ricerca e sulla base delle Politiche Linguistiche della Commissione Europea percorso formativo a carattere tematico-linguistico-didattico-metodologico scuola secondaria di secondo grado teachers Luigi Togliani and Claudio Borghi

2 Indice Modulo Strategies - Before Prerequisites Linking to Previous Knowledge and Predicting con questionari basati su stimoli relativi alle conoscenze pregresse e alle ipotesi riguardanti i contenuti da affrontare Italian/English Glossary Strategies During Video con scheda grafica Keywords riferite al video attraverso esercitazioni mirate Conceptual Map Strategies - After Esercizi: Multiple Choice Matching True or False Cloze Flow Chart Think and Discuss Summary per abstract e/o esercizi orali o scritti basati su un questionario e per esercizi quali traduzione e/o dettato Web References di approfondimento come input interattivi per test orali e scritti e per esercitazioni basate sul Problem Solving Answer Sheets 2

3 1 Strategies Before Prerequisites Trigonometry Geometrical optics basic concept of goniometric functions theorems about rightangled triangles light ray model rectilinear propagation of light Reflection and refraction of light 3

4 2 Strategies Before Linking to Previous Knowledge and Predicting Do you know the definitions of sine, cosine and tangent of an angle? Do you know the relationships between the sides of a right-angled triangle and the goniometric functions of the angles? Do you know the light ray model? 4

5 3 Strategies Before Italian/English Glossary Angolo Angolo di apertura di un prisma Angolo limite Coseno Indice di rifrazione Interfaccia Luce monocromatica Mezzo Normale Ottica geometrica Raggio incidente Raggio riflesso Raggio rifratto Riflessione Riflessione totale Rifrazione Seno Superficie di incidenza Tangente Vuoto Angle Apex angle of a prism Critical angle Cosine Index of refraction Interface Monochromatic light Medium Normal Optical geometry Incident ray Reflected ray Refracted ray Reflection Total internal reflection Refraction Sine Incidence surface Tangent Vacuum 5

6 4 Strategies During Keywords 1) Circle the optical concepts or phenomena: impact incidence ray reflection concentration osmosis refraction dispersion depth altitude critical angle 2) Completion: The incident ray, the reflected ray, the ray and the.. to the surface at the point of the incidence lie in the same. Light can travel through... A light ray passing from one medium to another is partially reflected and partially.. The speed of light is lower than c in every... When an incident ray meets a surface between two mediums, the... ray belongs to the medium from which it comes. When an incident ray meets an incidence. between two mediums, it can the second medium. 6

7 5 Strategies During Conceptual Map Complete the conceptual map using the following words: θ 1 = θ 2 Snell s law total internal reflection critical angle Incidence on a surface between two mediums Rays of light travelling in a straight line reflection and refraction refraction reflection If n2 > n1 it is possible that the transmitted ray does not exist 7

8 6 Strategies After Multiple Choice 1. A ray of light forms an angle of 40 with the surface of a mirror. The value of the angle of reflection is: a. 40 b. 50 c. 0 d. none of these 2. Two mirrors are perpendicular (see figure). The 1 st mirror reflects the ray CA; the reflected ray meets the 2 nd mirror in E. The new ray ED E D a. is not parallel to CA b. may be perpendicular to AE c. is perpendicular to AE d. none of these A B C 3. See the figure of item 2. If BÂC = 70 then the value of AÊD is a. 70 b. 150 c. 130 d. none of these 4.- How many images given by the two mirrors AB and BC (BA is perpendicular to BC) can you see of the object in the figure? a. 2 b. 3 c. 4 d. none of these B A C 5.- A ray of light comes from medium 1 to medium 2 (see figure). The ray of reflection and the ray of refraction are perpendicular. If γ = 30 then a. β = 30 b. n 2 /n 1 is around 1,4 according to Snell s law c. n 2 /n 1 is around 1,9 according to Snell s law d. none of these 1 2 α β γ 8

9 6.- When light passes from medium 1 to medium 2 the ratio of the indices of refraction is n 2 /n 1 = 1.6. If the value of the angle of refraction is 20 then the value of the angle of reflection is about: a. 29 b. 31 c. 33 d. none of these 7.- A ray of light passes from water (index of refraction 1.33) to air. If the angle of incidence is 45 then a. the angle of refraction is about 70 b. the angle of refraction is about 32 c. there is not refraction but total internal reflection d. none of these 8.- The speed of light in vacuum is about 3,010 8 m/s. The speed of light in glass with index of refraction 1.5 is a m/s because the speed of light is always constant b m/s c. undefined because data are not enough d. none of these 9

10 7 Strategies After Matching Match the words on the right with the correct explanation on the left: 1. Angle of reflection 2. Index of refraction 3. Critical angle 4. Refraction 5. Total internal reflection 6. Image a. Speed of light in a vacuum / speed of light in medium b. A phenomenon that happens when a ray of light strikes a medium boundary with an angle of incidence greater than a certain angle c. The angle which the reflected ray makes to the normal d. When on object stands in front of a mirror e. An angle above which total internal reflection occurs f. A phenomenon that happens when a ray of light changes its direction when it passes from a medium to another one 10

11 8 Strategies After True or False State if the following sentences are true (T) or false (F). 1.- Light may pass through matter, but can t pass through vacuum. 2.- The speed of light has a finite value but it can t be measured. 3.- Light may be only reflected by a reflective surface like a mirror. 4.- A mirror may create images that can t be collected by a screen. 5.- A ray of light passes from water to air. The angle of incidence may be Two plane mirrors may form 5 images of an object. 7.- The index of refraction is always a number greater than When a ray of light passes from water (index of refraction 1.33) to glass (index of refraction 1.50) it can t be totally reflected. 9.- When a ray of light passes through a prism you may observe the dispersion of light A ray of light passes from medium 1 (n 1 =2.6) to medium 2 (n 1 =1.3). According to Snell s law: ϑ 1 =30 and ϑ 2 =60. T T T T T T T T T T F F F F F F F F F F 11

12 9 Strategies After Cloze Complete the text using the words or the expressions listed below. The phenomenon of refraction is the...[1] of light rays when they are passing through a surface between one...[2] material and another. It is described by Snell's law: where θ 1 is the angle between the ray and the...[3] in the first medium, θ 2 is the angle between the ray and the...[4] in the second medium, and n 1 and n 2 are the...[5]. A...[6] is an optical and meteorological phenomenon that causes a spectrum to appear in the sky when the Sun shines on droplets of water in the Earth's atmosphere. It usually takes the form of a single...[7]. The colour of the...[8] is... [9] on the upper side of the...[10] and... [11] on the inner side. The...[12] is caused by light being...[13] while entering the droplet. arc bending indices of refraction normal rainbow red refracted transparent violet 12

13 10 Strategies After Flow Chart Complete the following flow chart referring to a ray of light emitted by an optical source to a plane surface. You can use the terms listed below: the ray is refracted the ray is totally reflected start a ray of light input false crosses the surface between medium 1 and medium 2 true output output end 13

14 11 Strategies After Think and Discuss The following activity can be performed in a written or oral form. The teacher will choose the modality, depending on the ability (writing or speaking) that needs to be developed. The contexts in which the task will be presented to the students are: - the student is preparing an article about reflection and refraction of light - the student is preparing a report about experimental activities regarding reflection and refraction of light The student should: 1) Choose one of the following topics: Images with a plane mirror The refraction of light with a half cylindrical dioptre The dispersion of light with a prism 2) Prepare an article or a debate, outlining the main points of the argument, on the basis of what has been studied. 3) If the oral activity is the modality chosen by the teacher, the student should present his point of view on the topics to the whole class and a debate could start at the end of his presentation. 14

15 12 Strategies After Summary Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. In particular we observe the reflection of light. A mirror provides the most common model for specular light reflection. Reflection is principally described by the law of reflection, which states that the angle of incident equals the angle of reflection. Specular reflection forms images. Reflection from a flat surface forms a mirror image, which appears to be reversed from left to right because we compare the image we see to what we would see if we were rotated into the position of the image. Refraction is the change in direction of a wave due to a change in its speed. Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth. Refraction is described by Snell's law, which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence θ 1 and angle of refraction θ 2 is equivalent to the ratio of phase velocities (v 1 / v 2 ) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n 2 / n 1 ): The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary (see diagram illustrating Snell's law). Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle θ c is given by Snell's law, Rearranging Snell's Law, we get incidence. To find the critical angle, we find the value for θ i when θ t = 90 and thus sin θ t = 1. The resulting value of θ i is equal to the critical angle θ c.. 15

16 Now, we can solve for θ i, and we get the equation for the critical angle: If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. If for example, visible light were traveling through acrylic glass (with an index of refraction of 1.50) into air (with an index of refraction of 1.00), the calculation would give the critical angle for light from acrylic into air, which is Light incident on the border with an angle less than 41.8 would be partially transmitted, while light incident on the border at larger angles with respect to normal would be totally internally reflected. If the fraction n 2 / n 1 is greater than 1, then arcsine is not defined meaning that total internal reflection does not occur even at very shallow or grazing incident angles. So the critical angle is only defined when n 2 / n 1 is less than 1.. 1) Answer the following questions. The questions could be answered in a written or oral form, depending on the teacher s objectives. a. What does the law of reflection state? b. What is a mirror image? c. When can you see the phenomena of reflection and refraction at the same time? d. How can you define the phenomenon of refraction? e. What is the relationship between the angle of incidence and the angle of refraction? f. Why the angle of refraction is lower than the angle of incidence if the index of refraction of the second medium is greater than the index of refraction of the first medium? g. Why is it possible that the refracted ray does not exist? h. When does the critical angle exist? i. How can you calculate the critical angle? j. What happens when it occurs the phenomenon of the total internal reflection? 2) Write a short abstract of the summary (max 150 words) highlighting the main points of the video. 16

17 Web References Reflection, refraction and dispersion of light are treated in their different aspects, experimental and theoretical, in these sections, also with pictures, diagrams, tables and examples: Reflection: Refraction: Total internal reflection: Dispersion: 17

18 13 Activities Based on Problem Solving a) At the interface between two materials a light ray is at an angle of o with the interface on a side with an index of refraction of If the light is at an angle of o on the other side of the interface, what is the index of refraction on this side? b) A prism with an apex angle of 60.0 is constructed of glass with an index of refraction of The prism is illuminated with a narrow beam of collimated and monochromatic light, whose angle of incidence is of What is the angle δ between the direction of the emergent ray and the direction of the incident ray? c) A light ray hits a surface at an angle of o. The material on the other side of the surface has an index of refraction of 1.56 and the light is making an angle of o with the surface when it exits on this side. What is the index of refraction on the incident side of the interface? d) Will light traveling from glass to air reach the air if it approaches at a 38 o angle to the (flat) surface? Assume that the index of refraction of glass for the used light is

19 Answer Sheets Keywords: 1) incidence ray reflection refraction dispersion critical angle 2) refracted normal plane vacuum transparent refracted medium reflected surface enter Conceptual Map: Rays of light travelling in a straight line Incidence on a surface between two mediums reflection and refraction refraction reflection Snell s law If n2 > n1 it is possible that the transmitted ray does not exist θ 1 = θ 2 critical angle total internal reflection 19

20 Multiple Choice: 1b 2b 3d 4b 5d 6c 7b 8b Matching: 1c 2a 3e 4f 5b 6d True or False: 1F -2F - 3F - 4T - 5F - 6T - 7F - 8T - 9T - 10F Cloze: [1] bending; [2] transparent; [3] normal; [4] normal; [5] indices of refraction; [6] rainbow; [7] arc; [8] rainbow/arc; [9] red; [10] rainbow/arc; [11] violet; [12] rainbow;[13] refracted Flow Chart: the ray is totally reflected (output on the left) the ray is refracted (output on the right) Activities Based on Problem Solving a) 2.20 b) 30.0 c) 1.12 d) No, the angle of incidence is greater than the critical angle of 42 o. Materiale sviluppato da eniscuola nell ambito del protocollo d intesa con il MIUR 20