Philip P. answered • 03/20/18

Tutor

5.0
(476)
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

- θ
_{1}= the resolution for 542 nm = 0.08 arcsec - θ
_{2}= the resolution for 2.8 μm (2800 nm):

θ

_{2}/θ_{1}= (1.22·2800/d)/(1.22·542/d)θ

_{2}/(0.08 arcsec) = 2800/542Solve for θ

_{2}. 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 (θ

_{2}/θ_{1}), the conversion factors to arcseconds will cancel out in the same way that the**1.22**and the**d**canceled out.