Index of refraction and electromagnetic radiation

In summary, someone looking at an object from a boat at a depth of 2 meters would estimate that the object's apparent depth is 3.18 meters below the surface.
  • #1
physicsgal
164
0
"An electromagnetic radiation has a frequency of 5 x 10^14Hz

a) (wave in vacuum = 600nm)
b) (wave in water = 440 nm)
c) what is the index of refraction of a medium in which the speed of this radiation is 2.54 x 10^8 m/s?" :yuck:

so given: c = 2.54 x 10^8 m/s
f = 5 x 10^14Hz

required: ni

im not sure where to start on this one. any help will be appreciated.

~Amy
 
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  • #2
nevermind, i figured it out! :biggrin:

n = C/v

i don't know how to delete my original post.

~Amy
 
  • #3
physicsgal said:
"An electromagnetic radiation has a frequency of 5 x 10^14Hz

a) (wave in vacuum = 600nm)
b) (wave in water = 440 nm)
c) what is the index of refraction of a medium in which the speed of this radiation is 2.54 x 10^8 m/s?" :yuck:

so given: c = 2.54 x 10^8 m/s
f = 5 x 10^14Hz

required: ni

im not sure where to start on this one. any help will be appreciated.

~Amy

I can help with part c, the index of refraction is a ratio between the speed of light in a vacuum to the speed of light in the medium, so if we call the index of refraction n, then

n = (speed of light in vacuum)/(speed of light in medium)

For parts a and b, I think you can do a similar thing with a ratio of wavelengths, but I'm not sure if that's right or not so you may want to wait for someone to give you a more concrete answer about that.
 
  • #4
thanks dLeet!

im working on another problem if anyone can share some insight..

Someone is on their boat and their eye level is 1 m above the water. and they guess the apparent depth of an object is 2 m below the water surface. the angle of which the person is looking at the object is 45 degrees.

so ni = 1.00029 (air)
nR = 1.33 (water)

so is this just a matter of (2m x 1.33) + 1m = 3.66m actual depth? :confused:

~Amy
 
  • #5
ok.. did some reading and looks like i was wrong (surprise, surprise).

so i go:
sin 0i = (ni/nR) x sin 45 degrees
sin 0i = (1.00029/1.33) x sin 45 degrees
sin 0i = 0.5318
0i = 32.1 degrees

Dactual = 2.0/tan 32.1 degrees
= 3.18 meters

opinions?

~Amy
 

1. What is the index of refraction?

The index of refraction is a measure of how much light is slowed down as it travels through a medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.

2. How does the index of refraction affect the path of light?

The index of refraction determines the amount of bending or refraction that occurs when light travels through a medium. The higher the index of refraction, the more the light is slowed down and bent.

3. What factors affect the index of refraction?

The index of refraction is affected by the density and composition of the material. Generally, denser materials have higher refractive indices. The wavelength of light and temperature can also have an impact.

4. Can the index of refraction be less than 1?

No, the index of refraction cannot be less than 1. A value of 1 indicates that light is traveling at the same speed in the medium as it would in a vacuum. Values less than 1 are not physically possible.

5. How does the index of refraction relate to electromagnetic radiation?

The index of refraction is a property of the medium that affects how electromagnetic radiation, including visible light, travels through it. The index of refraction is used to calculate the speed of light in different materials and also plays a role in determining the angle of refraction when light passes through a medium.

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