Confused about this Optics problems Solution

[Xyius]

Homework Statement

The Lick Observatory has one of the largest refracting telescopes, with an aperture diameter of 36 in. and a focal length of 56 ft. Determine the radii of the first, second, and third bright rings surrounding the Airy disc in the diffraction pattern formed by a star on the focal plane of the objective.

Homework Equations

$$\frac{\pi}{\lambda}Dsin\theta=\gamma$$
Where \gamma is either the maxima (bright fringes) or minima (dark fringes) of the bessel function which occurs in the solution to the diffraction through a circular aperture.
$$r=f \theta$$
Where f is the focal length.
Maxima of Gamma function: 5.136,8.417,...

The Attempt at a Solution

This is not an attempt, this is part of the actual solution. I do not understand a certain aspect of it though.

So using the first equation above and solved for sine. I came into a problem though. The problem doesn't give the wavelength! The solution just says..
"Thus for wavelength of 550nm..."
And then they plug it in. Where did this come from?!

Thanks :D

 

[Simon Bridge]

550nm is green light - right in the middle of the visible spectrum and thus in the middle of the fringes/rings.

This sort of thing is common - IRL you are unlikely to have all the information you need to do a calculation right then and there. It may be difficult to get a figure too. So you have to make a reasonable guess. If you knew the spectra of the star in question, you would pick a different wavelength perhaps but you are only told that it is visible.

 

[Xyius]

Thank you very much! That makes perfect sense :]

 

[Simon Bridge]

No worries then - have fun :)