Question

AMichelson stellar interferometer is used to determine the apparent diameter of a star. The fringe pattern disappears when the adjustable mirrors are at a separation of 5 m. What is the
angular diameter of the star?

Answer 1

Answer on Question #54966 – Physics / Astronomy | Astrophysics

Question:

A Michelson stellar interferometer is used to determine the apparent diameter of a star. The fringe pattern disappears when the adjustable mirrors are at a separation of $5\mathrm{m}$. What is the angular diameter of the star?

Solution:

We can use the next equation:

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

A value of $\lambda$ is $5 \times 10^{-4} \, \mathrm{mm}$ and $d = 5 \, \mathrm{m}$ or $5 \times 10^{3} \, \mathrm{mm}$. Now we can use this:

$$\theta = \frac{1.22 \times 5 \times 10^{-4}}{5 \times 10^{3}} = 1.22 \times 10^{-7} \, \mathrm{rad}$$ $$\theta = 1.22 \times 10^{-7} \, \mathrm{rad}$$ $$\theta = 0.025 \, \mathrm{arc} \, \mathrm{sec}$$

Answer: $\theta = 0.025$ arc sec.

https://www.AssignmentExpert.com