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A LevelPhysicsCambridge (CIE)Revision Notes24. Medical PhysicsProduction & Use of UltrasoundIntensity Reflection Coefficient

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Intensity Reflection Coefficient (Cambridge (CIE) A Level Physics): Revision Note

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Intensity reflection coefficient

  • The intensity reflection coefficient α is defined as:

    The ratio of the intensity of the reflected wave relative to the incident (transmitted) wave

  • This can be calculated using the fraction:

alpha space equals space fraction numerator I subscript R space over denominator I subscript 0 end fraction space equals space fraction numerator open parentheses Z subscript 2 space minus space Z subscript 1 close parentheses squared space over denominator open parentheses Z subscript 2 space plus thin space Z subscript 1 close parentheses squared end fraction

  • Where:

    • α = intensity reflection coefficient

    • IR = intensity of the reflected wave (W m-2)

    • I0 = intensity of the incident wave (W m-2)

    • Z1 = acoustic impedance of one material (kg m-2 s-1)

    • Z2 = acoustic impedance of a second material (kg m-2 s-1)

  • This equation will be provided on the datasheet for your exam

  • This ratio shows:

    • If there is a large difference between the impedance of the two materials, then most of the energy will be reflected

    • If the impedance is the same, then there will be no reflection

Coupling medium

  • When ultrasound is used in medical imaging, a coupler is needed between the transducer and the body

  • The soft tissues of the body are much denser than air

  • If air is present between the transducer and the body, then almost all the ultrasound energy will be reflected

  • The coupling gel is placed between the transducer and the body, as skin and the coupling gel have a similar density, so little ultrasound is reflected

    • This is an example of impedance matching

Worked Example

A beam of ultrasound is incident at right angles to a boundary between two materials as shown in the diagram.

WE - Intensity reflection coefficient question image, downloadable AS & A Level Physics revision notes

The materials have acoustic impedances of Z1 and Z2. The intensity of the transmitted ultrasound beam is IT, and the reflected intensity is IR.

(a) What is the relationship between I, IT and IR? 

(b) Use the data from the table to determine the reflection coefficient α for a boundary between

(i)  gel and soft tissue

(ii)  air and soft tissue 

(c) Explain why gel is usually put on the skin during medical diagnosis using ultrasound. 

medium

speed of ultrasound / m s–1

acoustic impedance / kg m–2 s–1

air

330

4.3 × 102

gel

1500

1.5 × 106

soft tisuse

1600

1.6 × 106

bone

4100

7.0 × 106

Answer:

Part (a)

State the relationship between I, IT and IR:

Incident intensity = Transmitted intensity + Reflected intensity

I space equals space I subscript T thin space plus space I subscript R

Part (b)(i)

Step 1: Write down the equation for intensity reflection coefficient α

alpha space equals space fraction numerator open parentheses Z subscript 2 space minus space Z subscript 1 close parentheses squared space over denominator open parentheses Z subscript 2 space plus thin space Z subscript 1 close parentheses squared end fraction

Step 2: Write down the acoustic impedances for gel and soft tissue

  • Gel, Z1 = 1.5 × 106 kg m-2 s-1

  • Soft tissue, Z2 = 1.6 × 106 kg m-2 s-1

Step 3: Calculate the intensity reflection coefficient

alpha space equals space fraction numerator open parentheses 1.6 space cross times space 10 to the power of 6 space minus space 1.5 space cross times space 10 to the power of 6 close parentheses squared space over denominator open parentheses 1.6 space cross times space 10 to the power of 6 space plus space 1.5 space cross times space 10 to the power of 6 close parentheses squared end fraction space equals space fraction numerator open parentheses 0.1 close parentheses squared space over denominator open parentheses 3.1 close parentheses squared end fraction space equals space 0.001

  • This result means that only 0.1% of the incident intensity will be reflected, with the remaining being transmitted

Part (b)(ii)

Step 1: Write down the acoustic impedances for air and soft tissue

  • Air, Z1 = 4.3 × 102 kg m-2 s-1

  • Soft tissue, Z2 = 1.6 × 106 kg m-2 s-1

Step 2: Calculate the intensity reflection coefficient

alpha space equals space fraction numerator open parentheses 1.6 space cross times space 10 to the power of 6 space minus space 4.3 space cross times space 10 squared close parentheses squared space over denominator open parentheses 1.6 space cross times 10 to the power of 6 space plus thin space 4.3 space cross times space 10 squared close parentheses squared end fraction space almost equal to space fraction numerator open parentheses 1.6 space cross times space 10 to the power of 6 close parentheses squared space over denominator open parentheses 1.6 space cross times space 10 to the power of 6 close parentheses squared end fraction space almost equal to space 1

  • This result means that 100% of the incident intensity will be reflected, with none being transmitted

Part (c)

  • At the air-soft tissue boundary, the intensity reflection coefficient is α ≈ 1

    • Therefore, without gel, there is almost complete reflection, no ultrasound is transmitted through the skin

  • Therefore, the gel enables almost complete transmission of the ultrasound through the skin, with very little reflection

    • At the gel-soft tissue boundary, the intensity reflection coefficient is α = 0.001

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.