[HW question] Image size difference of two light emitting nanospheres

[rinalai]

Homework Statement

Suppose two light emitting nanospheres with diameters of 50nm and 100nm, respectively, are observed with a microscope. Can they be seen at all and if yes, what will be the size differences of their images (i.e. is the image of sphere 1 smaller, equal or larger than that of sphere 2)? Why?

Relevant Equations

(not sure)

I wonder if this question is about two-point resolution or magnification...
Would someone here be so kind as to offer some guidance on this question? Thank you!

 

[phystro]

So if you don't specify how strong is your microscope, I don't think that this question can be answered.

 

[rinalai]

The power of the microscope was not given by the professor...
It seems that there's some requirements missing in the question.

 

[phystro]

The question might be asking about encyclopedic knowledge, of what is the smallest visible object with a light microscope - the so called resolution limit. The resolution limit of the light microscope cannot be smaller than half of the wavelength of the visible light, which is about 380 to 700 nanometers.
So, both spheres would be invisible from the microscope, since 380/2= 190nm (therefore 190nm is the resolution limit for visible light microscopes, and anything below 190nm would be invisible).

 

[rinalai]

Thank you so much for helping out!
I had a discussion with my professor, and here is the explanation from him:

"Even with the highest possible resolution of optical microscopes, the size of the spheres cannot be resolved; both are sub-resolution spheres.
Can they be seen? Yes, since they emit light they can be seen.
How will their images look like? Both will generate Airy discs of effectively the same size as images."