IPhO 2022

Problem 1 (10 points) A Round Matter Determine the following quantities and give them rounded to whole numbers. a) The ratio of the airspeed of an aircraft in still air to the wind speed in the following case: for one leg the aircraft needs 7.0 hours flying against the wind, while it covers the same distance on the return leg with the wind in 6.0 hours. b) The acceleration (in multiples of g = 9.81 ms-2) of a wet sock in a washing-machine drum with a diameter of 40 cm in the gentle spin cycle at 600 revolutions per minute. c) The smallest resistance value (in $Ω$ ) that can be achieved by combining the following resistors without short-circuiting them: one resistor each of $100Ω$ , $220Ω$ , $330Ω$ and 360 $Ω$ . d) The mass of ice (in kg) that warms from an initial -10 $^{\circ} C$ to 10 $^{\circ} C$ by the supply of a quantity of heat of 2.4 MJ. Strung together correctly and completed with the right power of ten and unit, the numbers represent the digits of a natural constant. State this natural constant together with its name.

Topic: Newtonian Mechanics, Circuits, Thermodynamics Metodi: Kinematic Equations, Equivalent Circuit Reduction, First Law of Thermodynamics, Order-of-Magnitude Estimation Competenze: Estimation & Approximation, Physical Reasoning, Mathematical Modeling Objects: Resistor Fonte: Testo (PDF) — p.2

Problema 1 (10 punti) Una questione rotonda Determina le seguenti quantità e diale arrotondate a numeri interi. a) Il rapporto tra la velocità d’aria di un aereo in aria ferma e quella del vento nel caso seguente: Gli aerei hanno bisogno di 7.0 ore di volo contro il vento, mentre coprono la stessa distanza sul ritorno con il vento in 6.0 ore. b) L’accelerazione (in multiples di g = 9.81 ms-2) di una calzatura bagnata in un lavandino con un diametro di 40 cm in Il ciclo di spin gentile a 600 rivoluzioni al minuto. c) Il valore di resistenza più piccolo (in $Ω$ ) che può essere raggiunto combinando le seguenti resistori senza short-circuiting: un resistore di $100Ω$ , $220Ω$ , $330Ω$ e 360 $Ω$ . d) La massa di ghiaccio (in kg) che si riscaldano da un iniziale -10 $^{\circ} C$ a 10 $^{\circ} C$ per la fornitura di una quantità di calore di 2,4 MJ. Strung together correctly and completed with the right power of ten and unit, i numeri rappresentano i numeri di una costante naturale. State this costante naturale insieme al suo nome.

The following points are added: A round matter Determine the following quantities and give them rounded to whole numbers. (a) The ratio of the airspeed of an aircraft in still air to the wind speed in the following case: aircraft needs 7.0 hours flying against the wind, while it covers the same distance on the return leg with the wind in 6.0 hours. b) The acceleration (in multiples of g = 9.81 ms-2) of a wet sock in a washing machine drum with a diameter of 40 cm in The gentle spin cycle at 600 revolutions per minute. (c) The smallest resistance value (in $Ω$ ) that can be achieved by combining the following resistors without short-circuiting them: One resistor each of $100Ω$ , $220Ω$ , $330Ω$ and 360 $Ω$ . d) The mass of ice (in kg) that warms from an initial -10 $^{\circ} C$ to 10 $^{\circ} C$ by the supply of a quantity of heat of 2.4 MJ. Strung together correctly and completed with the right power of ten and unit, the numbers represent the digits of a natural constant. State this Natural constant together with its name.

Problem 2 (10 points) Tipping Iceberg Tabular icebergs have a relatively flat top and steep edges. They form by breaking off from ice shelves and can be very large. Just as with other icebergs, in a floating tabular iceberg the largest part of the ice lies not above but below the water. In the following, consider an approximately box-shaped tabular iceberg of height H, length L and width B. For the density of ice and seawater use the approximate values $ρE i s$ = 0.9 $\cdot$ 103 kg m-3 and $ρ W a sser$ = 1.0 $\cdot$ 103 kg m-3. a) Determine what fraction of the height H of the iceberg lies below the water surface. When breaking off from an ice shelf, relatively narrow tabular icebergs can form, in which the width B is smaller than the height H. Such an iceberg can tip onto its side. b) Show that for a narrow tabular iceberg it is energetically more favourable to tip onto its side. Determine for which ratio of width to height the most energy is released by tipping over. Assume here that L

H. The released energy can lead to high waves, which can also become dangerous for ships in the vicinity. Alongside is a photo of the passenger ship Fram in front of an iceberg. The ship has a length of about 114 m. c) Estimate the energy that would be released when the iceberg tips over. To do this, simplify by assuming that the photo of the ship was taken from a great distance and that the iceberg has approximately the shape of a tabular iceberg whose length and width are equal. Calculate the mass of TNT that would have to be detonated to release the same energy. Photo of a tabular iceberg (by Andrew Shiva, CC BY-SA 4.0). Photo of a ship in front of an iceberg (by Kim Hansen, CC BY-SA 4.0). Best to hang the problems directly next to the poster!

Topic: Fluid Mechanics, Conservation of Energy, Newtonian Mechanics Metodi: Hydrostatic Equilibrium, Energy Conservation Method, Physical Modeling, Order-of-Magnitude Estimation Competenze: Estimation & Approximation, Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.2

Problema 2 (10 punti) Tipping Iceberg Gli iceberg tabulari hanno una sommità relativamente piatta e bordi ripidi. - Sono formate dalla rottura da piante di ghiaccio e possono essere molto grandi. Come con altri iceberg, in un iceberg tabulare galleggiante la più grande parte del ghiaccio non è sopra, ma sotto l’acqua. In the following, considerate un iceberg tabular di altezza H, lunghezza L e larghezza B. Per la densità di uso di ghiaccio e acqua di mare i valori approssimativi $ρE i s$ = 0,9 $\cdot$ 103 kg m-3 e $ρ W a sser$ = 1,0 $\cdot$ 103 kg m-3. a) Determina quale frazione dell’altezza H dell’iceberg si trova al di sotto del superficie acquatica. Quando si rompe da un ripiano di ghiaccio, gli iceberg tabulari possono essere relativamente stretti. forma in cui la larghezza B è inferiore alla altezza H. Cercare un iceberg può puntare sul suo lato. b) Show that for a narrow tabular iceberg it is energetically more favourable to tip

E’ il mio amico. Determine for which ratio of width to height the La maggior parte dell’energia viene rilasciata con il tipping over. Supponiamo che l

H. L’energia rilasciata può portare ad alte onde, che possono anche diventare pericolose per le navi.

In prossimità. Accanto è una foto della nave passeggeri Fram di fronte a un iceberg. La nave ha una lunghezza di circa 114 metri. c) Estimare l’energia che sarebbe rilasciata quando l’iceberg punta
Non è più così. Per fare questo, semplificare assumendo che la foto della nave è stata presa da un grande Distanza e che l’iceberg ha circa la forma di un iceberg tabular la cui lunghezza e larghezza sono uguali. Calcolo la massa di TNT che dovrebbe essere detonata per rilasciare lo stesso energia. Foto di un iceberg tabular (di Andrew Shiva, CC BY-SA 4.0). Foto di una nave di fronte ad un iceberg (di Kim Hansen, CC BY-SA 4.0). Best to hang i problemi direttamente vicino a Il poster!

Problem 2 (10 points) Tipping the iceberg Table icebergs have a relatively flat top and steep edges. They It’s a form by breaking off from ice shelves and can be very large. Just like with other icebergs, in a floating tabular iceberg the largest part of the ice lies not above but below the water. In the following, consider an approximately box-shaped tabular iceberg of height H, length L and width B. For the density of ice and seawater use The approximate values $ρE i s$ = 0.9 $\cdot$ 103 kg m-3 and $ρ W a sser$ = 1.0 $\cdot$ 103 kg m-3. (a) Determine what fraction of the height H of the iceberg lies below the water surface. When breaking off from an ice shelf, relatively narrow tabular icebergs can form, in which the width B is smaller than the height H. Search for an iceberg Can tip onto its side. b) Show that for a narrow tabular iceberg it is energetically more favourable to tip On its side. Determine for which ratio of width to height the Most energy is released by tipping over. Assume here that L

H. The released energy can lead to high waves, which can also become dangerous for ships In the vicinity. Alongside is a photo of the passenger ship Fram in front of an iceberg. The ship has a length of about 114 m. (c) Estimate the energy that would be released when the iceberg tips

I’m not going to. To do this, simplify by assuming that the photo of the ship was taken from a great distance and that the iceberg has approximately the shape of a tabular iceberg whose length and width are equal. Calculate The mass of TNT that would have to be detonated to release the same Energy. Photo of a tabular iceberg (by Andrew Shiva, CC BY-SA 4.0) Photo of a ship in front of an iceberg (by Kim Hansen, CC BY-SA 4.0). Best to hang The problems directly next to The poster!

Problem 3 (10 points) Inclined Plane A small sled with a mass of 280 g slides down an inclined plane, as sketched below. At the bottom of the inclined plane an approximately massless spring is attached. The following diagram shows the velocity of the sled along the inclined plane as a function of time after release at the upper end of the inclined plane. The acceleration due to gravity is g = 9.81 ms-2. a) Describe the motion of the sled using the graph. Determine the accelerations of the sled while it slides on the plane. From this and from further information that can be read off the graph, important information about the system can be obtained. b) Determine, at least approximately, at least four quantities that describe the setup of the system.

Topic: Newtonian Mechanics, Oscillations & Waves Metodi: Kinematic Equations, Free-Body Diagram, Hooke’s Law, Experimental Data Analysis Competenze: Graph Linearization, Physical Reasoning, Experimental Data Analysis Objects: Inclined Plane, Spring, Block Fonte: Testo (PDF) — p.3

Problema 3 (10 punti) Piani inclinati Una piccola slitta con una massa di 280 g slide giù in piano inclinato, come schizzolato di seguito. Al fondo del piano inclinato è attaccato una sorgente approximately massless. Il diagramma seguente mostra la velocità del sled lungo il piano inclinato come funzione di Time after release all’estremità superiore del piano inclinato. L’accelerazione dovuta alla gravità è g = 9,81 ms-2. a) Descrivere il movimento del sled usando il grafico. Determina le accelerazioni del sled mentre scivola sul piano. Da questo e da ulteriori informazioni che possono essere lette dal grafico, possono essere ottenute informazioni importanti sul sistema. b) Determinare, almeno approssimativamente, almeno quattro quantitativi che descrivono la configurazione del sistema.

Problem 3 (10 points) Inclined planes A small sled with a mass of 280 g slides down an inclined plane, as sketched below. At the bottom of the inclined plane an approximately massless spring is attached. The following diagram shows the velocity of the sled along the inclined plane as a function of Time after release at the upper end of the inclined plane. The acceleration due to gravity is g = 9.81 ms-2. (a) Describe the motion of the sled using the graph. Determine the accelerations of the sled as it slides on the plane. From this and from further information that can be read off the graph, important information about the system can be obtained. (b) Determine, at least approximately, at least four quantities that describe the setup of the system.

Problem 4 (10 points) Tasty Lens The aim of this problem is the experimental determination of the refractive index of jelly, also called gelatin dessert. To do this, obtain a jelly mix for stirring up and pour the still-liquid jelly mass into a cylindrical, transparent vessel to set. Alternatively, you can also buy a ready-made jelly in a transparent and preferably cylindrical container. The jelly in the vessel forms a cylindrical lens. If you let the light of a light source fall onto the lens from the side, you can produce an image of the light source on a screen on the other side. Using the jelly lens, experimentally determine the refractive index of the jelly. Carry out your measurements several times and estimate the uncertainty of your result. Hints: It is helpful to choose as symmetric an arrangement of the ray path as possible, which allows the use of the lensmaker’s equation for thin lenses. In the case where the thickness of the vessel wall is small compared with the diameter of the lens, you can assume that the vessel is part of the lens. Junior problem (10 points) Strange Reflection The photo alongside shows a house facade and its reflection in a flat water surface. Something about the reflection appears strange, however. Describe what is unexpected about the reflection of the sun. Using a sketch that reproduces the ray paths of the light, explain how the described phenomenon may have come about. The photo can be downloaded in better resolution on the website of the PhysicsOlympiad at www.ipho.info. Example of the experimental material. Photo of the house facade and its mirror image. Sled Spring Not-to-scale sketch of the system consisting of sled, inclined plane and spring. 0 2 4 6 8 10 12 $- 1, 0$ $- 0, 5$ 0,0 0,5 1,0 t/s v /(ms $- 1$ ) Velocity of the sled. Register now at www.ipho.info www.ipho.info for the competition! scienceolympiaden.de Show your talent! Students If you are a student, the IPhO and the PhysicsOlympiad in Germany offer you many opportunities to engage intensively with physics questions, to experience physics as an exciting scientific discipline, to test your own limits and not least to get to know interesting people. For the competition rounds there are learning materials and training problems that help you to deepen your knowledge and problem-solving skills. At the seminars you meet many other students enthusiastic about physics. Taking part is therefore worthwhile in any case and regardless of whether you make it into the higher rounds. What matters is taking part. Successfully completing the first round is already a special achievement and a genuine distinction. So, just be brave! Teachers As a teacher, with the problems of the PhysicsOlympiad you can offer a challenge to students who are particularly capable or interested in physics and encourage them to engage more deeply with physics topics. In this way the PhysicsOlympiad can serve as an instrument of individual support. In particular, the problems of the 1st round are suitable not only for the best in a class.

With its varied offerings, the PhysicsOlympiad aims to appeal broadly to interested young people and to inspire them lastingly for the natural sciences. This is served by support offerings such as the Orpheus seminars and the accompanying materials for the 1st round, with which we want to support you in introducing topics of the PhysicsOlympiad. So feel free to encourage your students to take part; for only those who do not take part can lose. Schools Schools can sharpen their profile by encouraging participation in competitions and use them in the sense of an enrichment as a complement to school offerings. Competitions provide varied, differentiated learning environments for participating students. In the area of STEM subjects, the Olympiads, at least in the later rounds, represent a competition aimed at particularly motivated and high-achieving young people. Nevertheless, taking part also in the entry rounds is not only worthwhile, but can also contribute to a lasting motivation for STEM topics. Offerings such as the Orpheus seminars allow the support of a large number of participants. In many federal states, by the way, participation can be recognised as a special learning achievement or specialist/seminar paper of your students for the Abitur. Interested in more than physics? The IPhO is one of the six nationwide scientific student competitions organised by the IPN — the ScienceOlympiads. Besides the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO) and Physics (IPhO), these include the International JuniorScienceOlympiad (IJSO), the European ScienceOlympiad (EUSO) as well as the Federal Environment Competition (BUW). Together they address students from the beginning of secondary school until after the end of their school years and, with close networking, offer the possibility of lasting support of scientific abilities and interests. Further information can be found at www.scienceolympiaden.de. Many good reasons to take part in the PhysicsOlympiad Dear students, dear teachers, dear parents, rarely has there been so much talk about research and science as in the past weeks and months. The coronavirus pandemic shows how important they are for society. They contribute to us getting well through this enormous crisis. Already now we owe a great deal to science and research. Mathematics, computer science, natural sciences and technology — Germany as a land of innovation needs citizens who are at home in the STEM subjects. It needs the optimism for progress that emanates precisely from these subjects. That is why we want to inspire even more young people for them. The Federal Ministry of Education and Research is committed to ensuring that they can discover the world of the natural sciences and its possibilities. For example, we support many student and youth competitions. Among them are the scientific competitions, the ScienceOlympiads and the Federal Environment Competition, all of which are organised by the Leibniz Institute for Science and Mathematics Education. The success is enormous: every year, nationwide, around 10 000 students from the 5th grade upwards register. Beyond everyday school life they can solve exciting problems and thus discover their talents. In this strenuous year too it is worthwhile to take part in the competitions, even though in-person events are cancelled because of the pandemic and selection rounds take place digitally. Problems, experiments and accompanying materials are available online. They are also interesting for teachers: they find suggestions for teaching — beyond the competition itself. Many experiments can also be carried out at home. I invite all students, their parents and the teachers to discover the ScienceOlympiads and the Federal Environment Competition for themselves. Good luck! And above all: have fun! Anja Karliczek Member of the German Bundestag Federal Minister of Education and Research Dear students, dear parents, dear teachers, supporting the next generation of scientists is a task that concerns us all. Children let

Topic: Geometric Optics Metodi: Snell’s Law, Thin Lens & Mirror Equation, Ray Tracing, Error Propagation Competenze: Experimental Data Analysis, Measurement & Instrumentation, Estimation & Approximation Objects: Lens, Screen Fonte: Testo (PDF) — p.3

Problema 4 (10 punti) Lente Gustosa

Lo scopo di questo problema è la determinazione sperimentale dell’indice di rifrazione della gelatina, comunemente nota come dessert in gelatina. A tale scopo, ottenete una miscela di gelatina da preparare e versate la massa di gelatina ancora liquida in un recipiente cilindrico trasparente per farla indurire. In alternativa, potete acquistare una gelatina già pronta in un contenitore trasparente e preferibilmente cilindrico. La gelatina nel recipiente forma una lente cilindrica. Se fate incidere la luce di una sorgente luminosa sulla lente da un lato, potete ottenere un’immagine della sorgente luminosa su uno schermo dall’altra parte.

Utilizzando la lente di gelatina, determinate sperimentalmente l’indice di rifrazione della gelatina. Eseguite diverse misurazioni e stimatene l’incertezza.

Consigli: È utile scegliere un’impiego del cammino ottico il più simmetrico possibile, che consenta l’utilizzo dell’equazione del costruttore della lente per lenti sottili. Nel caso in cui lo spessore delle pareti del recipiente sia trascurabile rispetto al diametro della lente, potete assumere che il recipiente faccia parte della lente.

Problema per giovani (10 punti) Strana Riflessione

La fotografia accanto mostra una facciata di casa e la sua immagine riflessa in una superficie d’acqua piana. Tuttavia, qualcosa nell’immagine riflessa appare strano.

Descrivete cosa di insolito c’è nella riflessione del Sole. Utilizzando uno schizzo che riproduca i cammini dei raggi luminosi, spiegate come possa essere nato il fenomeno descritto. La foto può essere scaricata con risoluzione migliore sul sito della Olimpiade Internazionale di Fisica all’indirizzo www.ipho.info. Esempio del materiale sperimentale. Foto della facciata di una casa e della sua immagine riflessa. Slitta Molla Schizzo non in scala del sistema composto da slitta, piano inclinato e molla. 0 2 4 6 8 10 12 $- 1, 0$ $- 0, 5$ 0,0 0,5 1,0 t/s v /(ms $- 1$ ) Velocità della slitta. Iscrizione immediata su www.ipho.info www.ipho.info per partecipare alla gara! scienceolympiaden.de Mostra il tuo talento!

Studenti Se sei uno studente, l’IPhO e la Olimpiade di Fisica in Germania ti offrono numerose opportunità per approfondire con impegno le domande di fisica, vivere la fisica come una disciplina scientifica affascinante, metterti alla prova e non ultimo conoscere persone interessanti. Per le varie fasi della gara sono disponibili materiale didattico e problemi di allenamento che ti aiutano a approfondire le tue conoscenze e abilità risolutive. Nei seminari incontrerai molti altri studenti appassionati di fisica. Partecipare è quindi sempre utile, indipendentemente dal raggiungere le fasi successive. Ciò che conta è partecipare. Superare con successo la prima fase rappresenta già un risultato speciale e una vera distinzione. Allora, non aver paura!

Insegnanti Come insegnante, con i problemi della Olimpiade di Fisica è possibile offrire una sfida agli studenti particolarmente dotati o appassionati di fisica e incoraggiarli a impegnarsi in modo più approfondito con gli argomenti della disciplina. In questo modo, la Olimpiade di Fisica può fungere da strumento di sostegno individuale.

In particolare, i problemi del primo turno sono adatti non solo ai migliori della classe.

Con la sua offerta variegata, la Olimpiade di Fisica mira a coinvolgere ampiamente i giovani interessati e a ispirarli in modo duraturo alle scienze naturali.

Ciò è favorito da offerte di sostegno come i seminari Orpheus e dai materiali accompagnatori per il primo turno, con cui vogliamo sostenervi nell’introduzione degli argomenti della Olimpiade di Fisica.

Sentitevi liberi quindi di incoraggiare i vostri studenti a partecipare; soltanto chi non si iscrive può perdere.

Scuole Le scuole possono rafforzare il proprio profilo incoraggiando la partecipazione a competizioni e utilizzarle nel senso di un’arricchimento, come complemento alle offerte scolastiche.

Le competizioni offrono ambienti di apprendimento variati e differenziati per gli studenti partecipanti.

Nel settore delle materie STEM, le Olimpiadi, almeno nei turni successivi, rappresentano una competizione rivolta a giovani particolarmente motivati e di alto livello. Tuttavia, partecipare anche ai turni iniziali non è soltanto utile, ma può contribuire anche a una motivazione duratura per gli argomenti STEM.

Offerte come i seminari Orpheus consentono di sostenere un gran numero di partecipanti. In molti stati federali, inoltre, la partecipazione può essere riconosciuta come un’attività formativa speciale o una tesina specialistica/semestrale per gli studenti che conseguono l’Abitur. Interessati a qualcosa oltre la fisica? L’IPhO è una delle sei competizioni scientifiche nazionali organizzate dall’IPN — le ScienceOlympiads. Oltre alle selezioni per le olimpiadi internazionali di Biologia (IBO), Chimica (IChO) e Fisica (IPhO), queste includono anche l’International JuniorScienceOlympiad (IJSO), l’European ScienceOlympiad (EUSO) e la Bundeswettbewerb Umwelt (BUW). Insieme, esse si rivolgono agli studenti dall’inizio della scuola secondaria fino dopo la fine degli studi, offrendo con una stretta collaborazione la possibilità di un sostegno duraturo delle capacità e degli interessi scientifici.

Ulteriori informazioni sono disponibili su www.scienceolympiaden.de. Molte buone ragioni per partecipare all’Olimpiade di Fisica Cari studenti, cari insegnanti, cari genitori, raramente si è parlato così tanto di ricerca e scienza come negli ultimi mesi. La pandemia da coronavirus dimostra quanto siano importanti per la società.

Contribuiscono a superare questa enorme crisi. Già ora dobbiamo molto alla scienza e alla ricerca.

Matematica, informatica, scienze naturali e tecnologia — la Germania, terra dell’innovazione, ha bisogno di cittadini a proprio agio nei settori STEM. Ha bisogno dell’ottimismo per il progresso che proprio da questi settori proviene. È per questo che vogliamo ispirare ancora di più i giovani. Il Ministero federale dell’Istruzione e della Ricerca si impegna affinché possano scoprire il mondo delle scienze naturali e le sue possibilità. Ad esempio, sosteniamo numerose competizioni per studenti e giovani. Tra queste ci sono le competizioni scientifiche, le ScienceOlympiads e il concorso federale per l’ambiente, tutte organizzate dall’Istituto Leibniz per l’educazione alla scienza e alla matematica. Il successo è enorme: ogni anno, in tutta la Germania, circa 10.000 studenti a partire dalla quinta elementare si iscrivono. Al di là della vita scolastica quotidiana, possono risolvere problemi affascinanti e scoprire così i propri talenti. Anche quest’anno impegnativo vale la pena partecipare alle competizioni, anche se gli eventi in presenza sono stati annullati a causa della pandemia e le selezioni si svolgono digitalmente. I problemi, gli esperimenti e i materiali accompagnatori sono disponibili online. Sono interessanti anche per gli insegnanti: trovano suggerimenti per l’insegnamento — oltre alla competizione stessa. Molti esperimenti possono essere effettuati anche a casa. Invito tutti gli studenti, i loro genitori e gli insegnanti a scoprire da soli le ScienceOlympiads e il concorso federale per l’ambiente. In bocca al lupo! E soprattutto: divertitevi! Anja Karliczek Membro del Bundestag tedesco Ministro federale dell’Istruzione e della Ricerca Cari studenti, cari genitori, cari insegnanti, sostenere la prossima generazione di scienziati è un compito che ci riguarda tutti. I bambini lasciano

Problem 4 (10 points) Tasty Lens

The goal of this problem is the experimental determination of the refractive index of jelly, also known as gelatin dessert. To achieve this, obtain a jelly mix for preparation and pour the still-liquid jelly into a cylindrical, transparent container to let it set. Alternatively, you may purchase a ready-made jelly that is in a transparent and preferably cylindrical container. The set jelly inside the vessel forms a cylindrical lens. When light from a light source is directed onto this lens from the side, an image of the light source can be formed on a screen located on the opposite side.

Using the jelly lens, experimentally determine the refractive index of the jelly. Perform your measurements multiple times and estimate the uncertainty in your result.

Hints: It is advantageous to set up the optical arrangement as symmetrically as possible, which allows application of the lensmaker’s equation for thin lenses. In cases where the wall thickness of the container is small compared to the lens diameter, you may assume that the container walls are part of the lens.

Junior problem (10 points) Strange Reflection

The photograph below shows a house façade and its reflection in a flat water surface. However, something about the reflection appears unusual.

Describe what is unexpected about the reflection of the sun. Using a sketch that accurately reproduces the light ray paths, explain how this phenomenon might have occurred. The photo can be downloaded in higher resolution on the website of the Physics Olympiad at www.ipho.info. Example of experimental material. Photo of the house facade and its mirror image. Sled Spring Not-to-scale sketch of the system consisting of sled, inclined plane, and spring. 0 2 4 6 8 10 12 $- 1, 0$ $- 0, 5$ 0,0 0,5 1,0 t/s v /(ms $- 1$ ) Velocity of the sled. Register now at www.ipho.info www.ipho.info for the competition! scienceolympiaden.de Show your talent!

Students If you are a student, the IPhO and the Physics Olympiad in Germany offer you many opportunities to engage intensively with physics problems, to experience physics as an exciting scientific discipline, to test your own limits, and not least to get to know interesting people. For the competition rounds there are learning materials and training problems that help you deepen your knowledge and problem-solving skills. At the seminars you meet many other students enthusiastic about physics. Participation is therefore worthwhile in any case, regardless of whether you reach the higher rounds. What matters is taking part. Successfully completing the first round is already a special achievement and a genuine distinction. So, just be brave!

Teachers As a teacher, you can use the problems from the Physics Olympiad to challenge students who are particularly capable or deeply interested in physics, encouraging them to engage more profoundly with the subject. In this way, the Physics Olympiad can serve as a tool for individual support.

In particular, the problems from the 1st round are suitable not only for the top students in a class.

Through its diverse range of offerings, the Physics Olympiad aims to appeal broadly to young people with a genuine interest in science and to inspire them lasting enthusiasm for the natural sciences.

This goal is supported by initiatives such as the Orpheus seminars and accompanying materials for the 1st round, which we provide to help you introduce Physics Olympiad topics in your teaching.

So please feel free to encourage your students to participate; only those who do not take part can lose.

Schools Schools can strengthen their profile by encouraging participation in competitions and using them as enriching supplements to regular school offerings.

Competitions provide varied, differentiated learning environments for participating students.

In the field of STEM subjects, the Olympiads—especially in later rounds—are aimed at particularly motivated and high-achieving young people. Nevertheless, participation even in the preliminary rounds is not only worthwhile but can also foster lasting motivation for STEM topics.

Initiatives such as the Orpheus seminars allow us to support a large number of participants. In many federal states, participation may also be recognised as a special learning achievement or specialist/seminar paper for your students’ Abitur.

Interested in more than physics?

The IPhO is one of the six nationwide scientific student competitions organised by the IPN — Science Olympiads. In addition to the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO), and Physics (IPhO), these include the International Junior Science Olympiad (IJSO), the European Science Olympiad (EUSO), as well as the Federal Environment Competition (BUW). Together, they address students from the beginning of secondary school until after the end of their school years and, through close networking, offer the possibility of lasting support for scientific abilities and interests.

Further information can be found at www.scienceolympiaden.de.

Many good reasons to take part in the Physics Olympiad

Dear students, dear teachers, dear parents, there has rarely been such extensive discussion about research and science as in the past weeks and months. The coronavirus pandemic demonstrates how crucial they are for society.

They contribute to helping us overcome this enormous crisis. We already owe a great deal to science and research.

Mathematics, computer science, natural sciences, and technology — Germany as a land of innovation needs citizens who are at ease with STEM subjects. It needs the optimism for progress that precisely emanates from these disciplines. That is why we want to inspire even more young people for them. The Federal Ministry of Education and Research is committed to ensuring that they can discover the world of natural sciences and its possibilities. For example, we support many student and youth competitions. Among them are the scientific competitions, the Science Olympiads, and the Federal Environment Competition, all of which are organized by the Leibniz Institute for Science and Mathematics Education. The success is enormous: every year, nationwide, around 10,000 students from the 5th grade upwards register. Beyond everyday school life they can solve exciting problems and thus discover their talents. In this strenuous year too it is worthwhile to take part in the competitions, even though in-person events are cancelled because of the pandemic and selection rounds take place digitally. Problems, experiments, and accompanying materials are available online. They are also interesting for teachers: they find suggestions for teaching — beyond the competition itself. Many experiments can also be carried out at home. I invite all students, their parents, and the teachers to discover the Science Olympiads and the Federal Environment Competition for themselves. Good luck! And above all: have fun! Anja Karliczek Member of the German Bundestag Federal Minister of Education and Research Dear students, dear parents, dear teachers, supporting the next generation of scientists is a task that concerns us all. Children let

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