# From the nature of light unit

1. Jan 22, 2010

### Ryan B

1. The problem statement, all variables and given/known data

Q: An electromagnetic radiation has a frequency of 5.00 x 10^14 Hz.
a) Calculate its wavelength in a vacuum, in meters and nanometers.
b) Calculate its wavelength in water.
c) Is this radiation visible? If so, what is its colour?
d) What is the index of refraction of a medium in which the speed of this radiation
is 2.54 x 10^8 m/s?

I just need help with e)

2. Relevant equations

3. The attempt at a solution

10. An electromagnetic radiation has a frequency of 5.00 x 1014 Hz.

a) Calculate its wavelength in a vacuum, in meters and nanometers.

Given: The speed of light in a vacuum is 3.00 x 108 m/s.

Required: the wavelength of electromagnetic radiation, that has a frequency of 5.00 x 1014 Hz, in a vacuum, in meters and nanometers.

Analysis: c=(f)(wavelength{vac}) and c=(n)(wavelength{med})
Therefore wavelength(vac) = (n)(wavelength{med}) and wavelength(med) = wavelength(vac)/n

Solution: λ = (3.00 x 108 m/s) / (5.00 x 1014 Hz)
Λ = 6.00 x 10-7 m or 600nm

b) Calculate its wavelength in water.

Given: wavelength = 0.6 x 10^-6m or 600nm
n = 1.33 for water

Required: wavelength(med)

Analysis: c=(f)(wavelength{vac}) and c=(n)(wavelength{med})
therefore wavelength(vac) = (n)(wavelength{med}) and
wavelength(med) = wavelength(vac)/n

Solution: wavelength(med) = (0.6 x 10^-6m)/1.33
= 4.51 x 10^-7 or 451 nm

Phrase: The wavelength in water of an electromagnetic radiation, that has a frequency of 5.00 x 1014 Hz, is 451 nm

c) Is the radiation visible? If so, what is its colour?

Yes, the radiation is visible as orange (in a vacuum), since orange has a range of 590nm to 610nm on the spectrum and violet (in water), since violet has a range of 400nm – 450nm.

d) What is the index of refraction of a medium in which the speed of this radiation is 2.54 x 108 m/s?

Given:
Speed of light: 3.00 x 108 m/s
Speed of radiation in the medium: 2.54 x 108 m/s

Required: the index of refraction.

Analysys: n = speed of light in a vacuum/speed of light in a medium

Solution: n = (3.00 x 108 m/s)/(2.54 x 108 m/s)
n = 1.18

The only searches that come back to me are bronze....HELP!

2. Jan 22, 2010

### rock.freak667

Search for the electromagnetic spectrum and see what the frequency/wavelength corresponds to.

3. Jan 22, 2010

### Ryan B

4. Jan 22, 2010

### Ryan B

was i wrong when i said bronze?

5. Jan 22, 2010

### rock.freak667

Where does it lie now?

6. Jan 22, 2010

### Ryan B

In the visible light spectrum

7. Jan 22, 2010

### rock.freak667

then you'd encounter it as light from where?

8. Jan 22, 2010

### Ryan B

Hydrogen gas, neon gas, sodium or mercury vapour?

9. Jan 22, 2010

### rock.freak667

....or from the sun...sunlight.