A narrow beam of ultrasonic waves reflects off the liver tumor illustrated in th

Question

A narrow beam of ultrasonic waves reflects off the liver tumor illustrated in the figure to the right. The speed of the wave is 10.0% less in the liver than in the surrounding medium. Determine the depth of the tumor. A 5 foot tall women is standing in front of the convex side of a spherical mirror. The diameter of the spherical mirror is 20 ft. (a) Use ray tracing to find the location, size, orientation, and type of image. Be sure to state these features next to your image. (b) Use the thin lens equation to calculate the magnification of the image. A person 1.6 m tall stands 3.2 m from a reflecting globe in a garden. (a) If the diameter of the globe is 18 cm, where is the image of the person, relative to the surface of the globe? (b) How large is the person's image? A beam of light propagates from point A in medium 1 to point B in medium 2, a shown in the figure to the right. The index of refraction is different in these two media; therefore, the light follows a refracted path that obeys Snell's law. (a) Calculate the time required for light to travel from A to B along the refracted path. (b) Compare the time found in part (a) with the time it takes for light to travel from A to B along a straight-line path. (Note that the time on the be- straight-line path is longer than the time on the refracted path. In general, the shortest time between two points in different media is along the path given by Snell's law.)

Explanation / Answer

Q1.

speed of the wave in any medium is given by v/n

where v=speed of the wave in vacuum

n=refraction index

here given that v/n=0.9*v

==>n=1/0.9=1.1111

if angle of refraction is theta,

using snell's law, 1*sin(50)=1.1111*sin(theta)

==>theta=43.586 degrees

let depth of the tumour is d meters.

then total distance between two waves=d*tan(theta)+d*tan(theta)

==>0.12 m=2*d*tan(43.586)

==>d=0.063 m

so depth of the tumour is 6.3 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.