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 :)

 

[asteriatic]

As a scientist, it is important to always pay attention to the given information and make sure all necessary variables are included in your calculations. In this case, the wavelength of 550nm is likely given in the problem statement or it may be a standard value commonly used in optics calculations. If it is not explicitly given, it is important to clarify with the source of the problem or make an assumption based on common values. It is also important to double check your calculations and make sure they are consistent with the given information.