CK-12-Physics-Concepts - Intermediate

http://www.ck12.org Chapter 12. Waves and Energy Transfer

We already understand that the change in the wave direction at the border depends on the difference between the two
velocities. This relationship is conveniently expressed in a mathematical relationship:

sinθr

sinθi

=

vr

vi

=

λr

λi

The ratio of the sine of the angle of refraction to the sine of the angle of incidence is the same as the ratio of the
velocity of the wave in the new medium to the velocity of the wave in the old medium and equal to the ratio of
wavelength (λ) in the old medium to the wavelength in the new medium.

Example Problem:A water wave with a wavelength of 3.00 m is traveling in deep water at 16.0 m/s. The wave
strikes a sharp interface with shallow water with an angle of incidence of 53. 0 ◦. The wave refracts into the shallow
water with an angle of refraction of 30. 0 ◦. What is the velocity of the wave in shallow water and what is its
wavelength in the new medium?

Solution:sinsinθθri=vvrisosin 30

◦

sin 53◦=

vr

16. 0 m/sandvr=^10.^0 m/s.

vr

vi=

λr

λiso

10. 0 m/s

16. 0 m/s=

λr
3. 00 mandλr=^1.^88 m.
Example Problem: The ratio of the sinθrto sinθiis 0.769. If the wavelength of a wave in a new medium is
5. 00 × 10 −^9 m, what is its wavelength in the original medium?

Solution:

0. 769 =

λr

λi

soλi=

5. 00 × 10 −^9 m

0. 769

= 6. 50 × 10 −^9 m

Summary

• When any wave strikes a boundary between media, some of the energy is reflected and some is transmitted.


• When a wave strikes the media interface at an angle, the transmitted wave will move in a different direction
  than the incident wave. This phenomenon is known as refraction.


• At any media interface,sinsinθθri=vvri=λλri

Practice

Questions