Question

1)which telescope, optical or X-ray, would have higher resolving power for the same aperture?
2)A supernova explosion takes place at the distance of 4 pc. If the absolute magnitude of the supernova is -25, calculate It's apparent magnitude. Will the supernova be brighter than the sun, justify the answer.

Answer 1

1. Resolving power is $\varphi = \frac{1.22\lambda}{D}$

Optical Resolving power is $\varphi_{1} = \frac{1.22*550*10^{-9}}{D}$

X-ray Resolving power is $\varphi_{2} = \frac{1.22*10^{-10}}{D}$

$\varphi_{1} > \varphi_{2}$ , So Optical Resolving power $>$ X-ray Resolving power

ANSWER: Optical Resolving power is higher

2.

Use Pogson's law:

$$m _ {1} - m _ {2} = - 2. 5 \lg \left(\frac {E _ {1}}{E _ {2}}\right)$$ $$m _ {1} - (- 2 5) = - 2. 5 \lg \left(\frac {1 0 ^ {2}}{4 ^ {2}}\right)$$ $$m _ {1} - (- 2 5) = - 5 \lg \left(\frac {1 0}{4}\right)$$ $$m _ {1} - (- 2 5) = - 1$$ $$m _ {1} = - 2 6$$

ANSWER: Apparent magnitude is $m_{1} = -26$ . Apparent magnitude for the sun is $m_{1} = -26.7$ . So the sun will be brighter.

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