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PHYS1210 Advanced Physics I

Question

Answered

Questions:

Q1. A medical ultrasound system produces sound waves of frequency 2.5 MHz. Use the information in the table below to answer the following questions.

  1. What are the wavelengths of the ultrasound waves in air, blood and bone?
  2. What is the reflection coefficient for a sound waves incident on the interface between muscle and bone?
  3. A layer of fat is sandwiched between two muscle layers so the reflections at each that the ultrasound produces interference. For a given layer thickness, standing waves are produced.
  • Assuming that the standing wave pattern is of the closed-closed type, draw the patterns for the fundamental and fifth harmonics.
  • For what layer thicknesses are standing waves achieved for the fundamental and fifth harmonics?

Medium

Density (kg/m3)

Speed of Ultrasound (m/s)

Air

1.3

330

Water

1000

1500

Blood

1060

1570

Fat

925

1450

Muscle (average)

1075

1590

Bone (average)

1650

4080


Q2. Optical fibers are used to transmit light over a flexible line and are used widely in applications such as in the data communications and keyhole surgery. Light of wavelength in vacuum 625 nm is incident on the fiber which has a core refractive index of ncore = 1.46.

 

  1. What is speed of the light in the core?
  2. What is the wavelength in the core?
  3. What is the frequency of the light in (i) in air and (ii) in the core?
  4. The fiber transmits 150 mW of the red light through it. How many photons per second is this?
  1. If the critical angle for reflection at the core boundary is 75°, what is the refractive index of the cladding?

Q3. The following figure shows the location of an object with respect to a diverging lens.

 

  1. Copy the diagram and show:
    • (1 mark) the path of a parallel ray from the top of the object through the lens;
    • (1 mark) the path of a ray through the centre of the lens;
    • (2 marks) and use these rays to identify the location of the image.
  2. Is the image real or virtual? State why.
  3. (5 marks) Given that the object is 4.7 m from the lens, and the magnification is 0.25, calculate the focal length of the lens.
  4. A person with myopia wears such lenses to correct for their vision of objects in the distance. The lenses are positioned 15 mm from the eyes. What is the far point for this person?

Q4. Red light is often chosen for some skin diagnostics as it transmits well through the top layers of the skin. In this question take the refractive index of skin as nskin = 1.36.

  1. (i) Explain what the Brewster angle means for unpolarised incident light.

(ii) In words and a diagram, indicate the direction of the polarization of the light reflected.

  1. What is the Brewster angle for the skin?
  2. Laser Doppler velocimetry is a technique for measuring blood flow in small blood vessels. Consider the case for a laser at 620 nm and frequency f0. The frequency shifts are very small, but are detectable in practice using interferometric techniques. If a red blood cell in the body “sees” a frequency fbthat is shifted in frequency due to the Doppler effect by

fb  f0 = 25 kHz

Calculate the velocity of the blood cell (speed and direction) with respect to the laser. You can assume that the cell is moving in a direction parallel to the beam.

Q5. Boron-12 decays via electron decay (e-) with a half-life of 20.2 ms. An anti-neutrino  is also produced.

  1. Complete the following reaction for this type of boron decay.

  1. There are initially N0= 3 ×1015 atoms of boron-12 in a sample.
    • How many are present after 0.55 s?
    • What are the initial and final activities?

PHYS1210 Advanced Physics I

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