Philip P. answered 03/20/18
Effective and Patient Math Tutor
The diffraction limited angular resolution, θ, of a telescope is given by:
θ = 1.22λ/d
where λ is the wavelength in cm and d is the telescope's diameter in cm. Let
- θ1 = the resolution for 542 nm = 0.08 arcsec
- θ2 = the resolution for 2.8 μm (2800 nm):
θ2/θ1 = (1.22·2800/d)/(1.22·542/d)
θ2/(0.08 arcsec) = 2800/542
Solve for θ2. The answer will have units of arcseconds ("). The longer wavelength (2800 nm) will have a larger angle of resolution because it diffracts more as it enters the telescope.
Strictly speaking, the formula for angular resolution will give an answer in radians, but since we are taking a ratio (θ2/θ1), the conversion factors to arcseconds will cancel out in the same way that the 1.22 and the d canceled out.