Question

We intend to observe two distant equal brightness stars whose angular separation is 50.0 × 10-7 rad. Assuming a mean wavelength of 550 nm, what is the smallest diameter objective lens that will resolve the stars (according to Rayleigh’s criterion)?

Answer 1

Answer:

13.4cm

Explanation:

According to Rayleigh’s criterion the angular resolution to distinguish two objects is given by:

$\theta=1.22\frac{\lambda}{b}$

θ = 50.0*10^-7 rad

λ: wavelength of the light = 550nm

b = diameter of the objective

By doing b the subject of the formula and replacing the values of the angle and wavelength you obtain:

$b=1.22\frac{\lambda}{\theta}=1.22\frac{550*10^{-9}m}{50.0*10^{-7}rad}=0.134m=13.4cm$

hence, the smallest diameter objective lens is 13.4cm

Answer 2

Answer:

0.134 m

Explanation:

Given:

θ=50.0 × 10-7

λ=550 nm

angular resolution to distinguish two objects developed by  Lord Rayleigh is given by:

θ= 1.22 λ/d

where λ is the wavelength of light (or other electromagnetic radiation) and D is the diameter of the aperture, lens, mirror, etc., with which the two objects are observed.

d= 1.22 λ/θ

d= (1.22 x 550 x $10^{-9}$) / 50 x $10^{-7}$

d=0.134 m

Therefore, the smallest diameter objective lens that will resolve the stars is 0.134 m