Calculating wavelengths of light

[YamunaVargr]

So. I need to calculate the wavelength of light that's required in order to excite the pi electrons of B-carotene from n=11 to n=13. The Length of the wavelength of L is 17.7 A.
I know how to look at the particle in a box method. And I know that the wavelength of light for B-carotene is 450, which is why a carrot is orange.
But I'm not quite grasping how to get the answer. 450 was incorrect.
Is there some math that I'm not realizing that I need to do?
I feel it should have something to do with the amount of pi electrons? Or the length of the conjugation chain?

Any input would be really helpful. This my first class on this subject, and I'm trying to stay caught up with all the new information.

 

[YamunaVargr]

If a photon comes from outside, or if the molecule is irradiated with light, electrons in the HOMO can be excited to the Lumo.
(I think that's what I'm going for.)
The energy difference between the two molecular orbitals or two states should correspond to the energy of the photon whose wavelength is 450 nm.

I feel like there should be a relatively simple way of going about this.