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

0.134 m

Step-by-step 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

Answer 2

13.4cm

Step-by-step explanation:

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

`\theta=1.22(\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(\lambda)/(\theta)=1.22(550*10^(-9)m)/(50.0*10^(-7)rad)=0.134m=13.4cm`

hence, the smallest diameter objective lens is 13.4cm