Question

The VLBA (Very Long Baseline Array) uses a number of individual radio telescopes to make one unit having an equivalent diameter of about 8000 km. This radio telescope is focusing radio waves of wavelength 2.0 cm. What would have to be the diameter of the mirror of a visible-light telescope focusing light of wavelength 582 nm so that the visible-light telescope has the same resolution as the radio telescope? Give an answer in m. Pay attention to the number of significant figures.

Answer 1

Answer:

d₂=232.8 m

Explanation:

We know that formula for resolution given as

θres = 1.22 λ/d

Where

λ=wavelength

d=diameter

Given that resolution should be same.So we can say that

1.22 λ₁/d₁= 1.22 λ₂/d₂

λ₁/d₁= λ₂/d₂

$d_2=\dfrac{\lambda _2}{\lambda _1}d_1$

Given that

λ₂=582 nm

λ₁=2 cm

d₁=8000 km

$d_2=\dfrac{582\times 10^{-9}\times 8000\times10^3}{0.02}\ m$

d₂=232.8 m