Light TPR Ch.11 Q#1

[Addallat]

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Q: In optics, spontaneous parametric down conversion is often used to create two photons from one photon. Thus, it is possible for a blue photon with a frequency of 700 THz to be split into two identical red photons when incident on a nonlinear crystal. What is the wavelength of the red photons with respect to the blue photon?


A. 2λB

B. 4λB

C. 1/2λB

D. 1/4λB


My reasoning:

Since the blue photon breaks into two red photons conservation of energy would mean each red photon is half the energy of a single blue photon
E(blue)=2E(red)

Since E = hf

then f(blue)= 2f(red)

Since

c/f(blue)=λ(blue)

and

c/2f(red) = λ(red)

Then isn't the wavelength of a red photon half the wavelength of a blue photon? I picked C. I don't get why the answer is A. Can somebody please identify where I'm going wrong

 

[Cawolf]

For starters, it is good to know that visible light has a wavelength of approximately 400 - 700 nm, with red being on the high end and blue low.

Mathematically I think you went wrong when you converted the frequency to wavelength.

E(blue) = 2E(red) E = hc/λ

hc/λ(blue) = 2hc/λ(red)

1/λ(blue) = 2/λ(red)

λ(red) = 2λ(blue)

So the wavelength is halved.

 

[Addallat]

For starters, it is good to know that visible light has a wavelength of approximately 400 - 700 nm, with red being on the high end and blue low.

Mathematically I think you went wrong when you converted the frequency to wavelength.

E(blue) = 2E(red) E = hc/λ

hc/λ(blue) = 2hc/λ(red)

1/λ(blue) = 2/λ(red)

λ(red) = λ(blue)/2

So the wavelength is halved.

It looks like you arrived at the same answer as I did (choice C). The book states the answer is A. Is the book wrong? I don't see how the wavelength of a red photon is twice that of a blue photon. Am I misinterpreting the question?

 

[Cawolf]

Oops I made a math error at the end.

It should have been:

1/λ(blue) = 2/λ(red)

λ(red) = 2λ(blue)

So the wavelength is doubled - which supports my initial statement.