1. An object is kept at a distance of 20 cm from a convex lens of focal length 10 cm. There is a second lens of focal length 10 cm separated by a distance of 25 cm from the first lens. What is the location of the final image? Mention the characteristics of the image formed.
2. You are given a convex lens and a plane mirror. Can you arrange them and construct an upright real image which is twice the size of the object? If yes How? If not Why not?
3. A person is in a car moving at certain speed between two hills separated by 2500m. When the car is at a distance of 1500m from one of the hills He gives a loud clap. He hears two echoes with duration of 5s of each other. Given the speed of sound to be 350 m/s. Given that the car is headed towards the hill B what is the speed of the car?
4. An object is kept at a distance of 15 cm from a convex lens of focal length 10 cm. There is a second lens of focal length 10 cm separated by a distance of 20 cm from the first lens. What is the location of the final image? Mention the characteristics of the image formed.
5. A real image of a square is formed from a convex lens as a distorted quadrilateral. Given the co-ordinates of the points of the quadrilateral find the location of the optic centre of the lens and its focal length. (The square lens and the quadrilateral image lie on the same plane) Co-ordinates | (35) (4 3) (40) (2 2) (Geometric solutions/constructions are appreciated. Numerical solutions can be really hard. Modified problem from IPhO Estonia 2012)
6. An object is kept at a distance of 5 cm from a convex lens of focal length 10 cm. There is a second lens of focal length 10 cm separated by a distance of 10 cm from the first lens. What is the location of the final image? Mention the characteristics of the image formed.
7. There are two mirrors between which the light bounces. The mirrors are separated by a distance d. It takes time t for the light to go from mirror A to mirror B and back to mirror A. Now the mirror system moves to the right with speed v. The speed of light c remains constant. What is the time taken for the light to bounce between the mirrors in terms of t c and v?
8. A ray of light bounces between 3 mirrors as in figure. Mirror B is at 120o to Mirror A and Mirror C is 100o to Mirror B. The light ray emerging from Mirror C is parallel to Mirror A. What is the angle of incidence at Mirror A?
9. You are given a glass slab with a mirror at the bottom. A light ray is incident on it undergoes refraction reaches the lower part end of the glass slab and get’s reflected back to the air medium. At the bottom the angle between the two rays is 60o. The angle between the incident ray and outgoing ray is 120o. What is the refractive index of the glass slab?
10. Draw a ray diagram for the following. (For all the images formed)
11. Consider 3 mirrors forming a right angle triangle. From the figure AB = AC = 20 cm. A ray of light is emitted from C and strikes point D on Mirror 1 (Mirror AB). AD = 15 cm. After being reflected by the mirrors many times can the ray ever arrive at point A? If yes what is the distance travelled by the whole ray from the beginning? If no why not?
12. Consider 3 mirrors forming a right angle triangle. From the figure AB = 3 AC = 1. A ray of light is emitted from C and strikes point D on Mirror 1 (Mirror AB). AD = 3/7 After being reflected by the mirrors many times if the ray arrives at B what is the distance travelled by the whole ray from the beginning? (Additional derivable information: ∠ = 60° ∠ = 30°)
13. Discussion problem: Effective Resistance What is the effective resistance of an infinite parallel circuit with resistors 2 4 8 16 32 ohm and so on in each of the branches? What is the effective resistance if the series was 2 3 4 5 6..? What’s the difference between the two cases? And can you explain correctly the reasons for the values in each case?
14. Power Dissipation: Given a resistor of 10Ω in series with a variable resistor R. What should be the value of R such that power dissipated by resistor R is maximum?
15. The circuit consists of 3 resistors in series as in figure. When the voltmeter is connected the across the AC the reading is 8V. When the same voltmeter is connected across BD the reading is 5V. What will the reading be on the voltmeter when connected across AD? Ans: 10 V. The voltmeter isn’t ideal and has a finite internal resistance of 12 ohms.
16. [IPhO 1967] Determine the resistance of the infinite periodic circuit. Each of the resistors has the value of 1 ohm. (Determine the resistance across A and B) Ans: (1+ √5)/2
17. [IPhO 1996] Determine the effective resistance across AB. (Every resistor is 1 ohm) Ans: 0.5 Ohm.
18. Knotted Field: Can magnetic fields produce knots? https://m.tau.ac.il/~kantor/QUIZ/98/A04.98.html
19. On Centrifugal force: https://m.tau.ac.il/~kantor/QUIZ/96/Q09.96.html A car participates in a race. Its tire explodes. What should be the speed of the car so that the tire does not become "flat"?
20. Missing Energy: https://m.tau.ac.il/~kantor/QUIZ/ A body starts sliding (from rest) without friction down a hill of height h. In the beginning the body has potential energy and no kinetic energy; at the end the body has only kinetic energy. It follows from energy conservation mgh=½mv2 that the velocity of the body at the bottom of the hill will be v=(2gh)1/2. Now consider the same process from a reference frame moving with velocity v (to the right) relative to the ground. In this reference frame the body in the beginning has potential energy mgh and kinetic energy (1/2)mv2 while at the end of the process both energies vanish. Where did the energy disappear? Give a detailed account of missing energy!
21. Benford’s Law: https://m.tau.ac.il/~kantor/QUIZ/00/A05.00.html Back side of the front cover of the Handbook of Chemistry and Physics lists 18 important fundamental (dimensional) constants and non-standard units such as speed of light, charge of an electron, Stephan-Boltzmann constant, electron volt, etc. Values of SEVEN out of 18 constants begin with digit 1. Why is digit 1 so prevalent in
