# Determining energy delivered from critical angle

• enc08
In summary, the conversation discusses the calculation of the critical angle at the urine-kidney stone interface and estimating the energy that will be delivered to the spherical stone. The data provided includes the density and speed of sound for urine and the kidney stone, as well as the diameter of the stone and the RMS intensity of the shock wave. The critical angle is calculated as 22°, but there is still a missing equation to determine the energy delivered.
enc08
Q. An ultrasound shock wave is incident on a kidney stone which is immersed in urine. Using the data below, calculate the critical angle at the urine-kidney stone interface, and thus estimate the energy that will be delivered to the spherical stone. Assume intensity is uniform across the stone.

$$\rho_{urine} = 1000kg/m^{3}, c_{urine} = 1000m/s, \rho_{stone} = 2000kg/m^{3}, c_{stone} = 4000m/s$$
Diameter of kidney stone $$d = 10mm$$
RMS intensity of shock wave $$I_{rms}=200MW/m^{2}$$

I have been able to do the first part of the question. I calculated the critical angle as $$\theta_{c}=arcsin(c_{urine}/c_{stone})=22°$$

However, I don't know how to go from this to determining the energy delivered.

Thanks for any input.

I don't know enough to answer the question, but I can see that you are missing some relevant equations. Do you have one for transmission coefficient?

## 1. How do you determine the critical angle?

The critical angle can be determined by using the equation sinθc = n2/n1, where θc is the critical angle, n1 is the refractive index of the first medium, and n2 is the refractive index of the second medium.

## 2. What is the significance of the critical angle?

The critical angle is the angle at which light is refracted at the interface between two different mediums. It is important because it determines whether light will be transmitted or reflected at the interface.

## 3. How does the energy delivered from the critical angle affect the refraction of light?

The energy delivered from the critical angle determines the intensity of the refracted light. As the critical angle increases, the amount of energy delivered decreases, resulting in a weaker refracted light beam.

## 4. Can the energy delivered from the critical angle be calculated for all materials?

Yes, the energy delivered from the critical angle can be calculated for all materials as long as the refractive indices of the two mediums are known.

## 5. How does the energy delivered from the critical angle relate to total internal reflection?

The energy delivered from the critical angle is directly related to total internal reflection. When the angle of incidence is greater than the critical angle, total internal reflection occurs, and no light is transmitted through the interface. This is because all of the energy is reflected back into the first medium.