Snell's Law for Light and Sound

In summary, when a laser beam and a sound wave with directional sources enter a liquid at a 60 degree angle from the horizontal surface, they both refract by the same amount. However, the light refracts to an angle of 74 degrees and the sound refracts to an angle of 26 degrees from the horizontal. This is due to the fact that the refractive index of the liquid is 1.8 for both light and sound. The relationship between speed and refractive index is also important to consider when understanding refraction.
  • #1
sparkle123
175
0
A laser beam and a sound wave from directional sources both enter a liquid at an angle of 60 degrees from the horizontal surface of the liquid. The speed of sound in the liquid is 1.8 times that of the speed of sound in air. For light, the refractive index of the liquid is 1.8. What happens?

Solution: The light refracts to an angle of 74° from the horizontal and the sound refracts to an angle of 26° from the horizontal.

I get that the beam and sound wave refract by the same amount since that both have a refractive index of 1.8 for the liquid. Also, my angle is different --> I get 69 degrees from the horizontal.
basically sin (40) = 1.8 sin (θ)
θ=21
 
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  • #2
If you are going to use the conventional equations in refraction then the angles should from the NORMAL... have you done that?
You should also read the information very carefully.
In one case they have given you speed information and in the other case they have given you a 'refractive index'... do you know the link between speed and refractive index?
 
  • #3
Yes, I did use the normal angles. I though speed is proportional to refractive index, like
v1/v2=n1/n2
 
  • #4
Hey sparkle123!

Speed is inversely proportional to refractive index.

And if the angle with the horizontal is 60 degrees, I'm afraid the angle with the normal is not 40 degrees...
 
  • #5
Wow I'm being awfully stupid! Thanks so much technician and I like Serena! :D
 

What is Snell's Law for Light and Sound?

Snell's Law is a principle named after Dutch mathematician Willebrord Snellius that describes the relationship between the angle of incidence and the angle of refraction of a wave passing through a boundary between two different mediums.

What does Snell's Law state?

Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of the wave in the two mediums. This can be expressed as n1sinθ1 = n2sinθ2, where n1 and n2 are the indices of refraction of the two mediums and θ1 and θ2 are the angles of incidence and refraction, respectively.

How is Snell's Law used in science?

Snell's Law is used in a variety of scientific fields, including optics, acoustics, and seismology. It is commonly used to predict the path of light or sound waves as they pass through different mediums, such as air, water, or glass. It is also used in the design of lenses and prisms for various optical instruments.

What are some real-life applications of Snell's Law?

Snell's Law has numerous practical applications in everyday life. It is used in the design of eyeglasses and contact lenses to correct vision, in the construction of underwater viewing devices, and in the development of fiber optic cables for telecommunication. Snell's Law is also essential in understanding the phenomenon of mirages and the refraction of light in the atmosphere.

How does Snell's Law differ for light and sound?

While the general principle of Snell's Law applies to both light and sound waves, there are some key differences in how it is applied. Light waves travel at a much faster speed than sound waves, so the indices of refraction for light are typically much smaller than those for sound. Additionally, the refraction of light is affected by the color or wavelength of the light, whereas sound waves of different frequencies typically have the same index of refraction.

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