IB Physics Galileo's Dying Breath

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A tutorial sheet of estimation questions is given below.

  1. Estimate how many molecules of air exhaled by Galileo during his dying breath you are likely to breathe during one breath. Surface area of the Earth = 5x108 km2.
  2. Estimate the time taken by a ray of light to travel the diameter of a hydrogen atom.
  3. Estimate the number of oxygen molecules in the air in a science laboratory.
  4. Estimate the number of atoms in a grain of sand.
  5. (After Enrico Fermi) Estimate the number of piano tuners in Chicago.
  6. Enrico Fermi was 10 miles from the blast site of the first atomic bomb. He released pieces of paper from rest and found that they travelled 2.5 m as the blast wave passed. Estimate the energy released in the blast. 1 ton of TNT yields 4x109 J of energy. [equivalent to 10 kilotons of TNT]

IB Physics Critical Angle

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A tutorial sheet on critical angle, a topic in SL waves, is given below.

  1. Define the term critical angle.
  2. Why can total internal reflection only occur if the wave speed in the first region is less than the wave speed in the second region?

  3. A diver is at a depth of 3.0 m in water of refractive index 1.3. The diver looks upwards. What is the diameter of the image of the horizon that they see?

  4. An electromagnetic wave strikes the end of an optical fibre at an angle 𝜽 to the normal. The refractive index of the cladding layer is n 2 and the refractive index of the optical fibre is n 1 . Show that the maximum value of 𝜽 which allows transmission of light along the fibre is given by sin𝜽 = (n1 2 -n2 2 ) 1/2 .

  5. For more applications of critical angle see Physics Education Vol 17, No 2, March 1982, p 86