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If an optical telescope focusing light of wavelength 550 nm has a per- fectly ground mirror, what would the minimum mirror diameter have to be so that the telescope could resolve a Jupiter-size planet around our nearest star, Alpha Centauri, which is about 4.3 light- years from earth? (Consult Appendix F.)

Answer :

Answer:

diameter = 197.35 m

Step-by-step explanation:

given data

wavelength = 550 nm = 550× [tex]10^{-9}[/tex] m

light year = 4.3

to find out

diameter D

solution

we know 1 light year have = 9.46 × [tex]10^{15}[/tex] m

so 4.30 light year = 40.678× [tex]10^{15}[/tex] m

and jupiter diameter is = 1.38 × [tex]10^{8}[/tex] m

now we find first angular resolution

that is = diameter / distance

so angular resolution = 1.38 × [tex]10^{8}[/tex]  /  40.678× [tex]10^{15}[/tex]

angular resolution = 3.40 × [tex]10^{-9}[/tex]

so diameter formula is

diameter = 1.22 × wavelength / angular resolution

diameter = 1.22 × 550 × [tex]10^{-9}[/tex]  / 3.40 × [tex]10^{-9}[/tex]

diameter = 197.35 m

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