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.)

diameter = 197.35 m

Step-by-step explanation:

given data

wavelength = 550 nm = 550× m

light year = 4.3

to find out

diameter D

solution

we know 1 light year have = 9.46 × m

so 4.30 light year = 40.678× m

and jupiter diameter is = 1.38 × m

now we find first angular resolution

that is = diameter / distance

so angular resolution = 1.38 ×  /  40.678×

angular resolution = 3.40 ×

so diameter formula is

diameter = 1.22 × wavelength / angular resolution

diameter = 1.22 × 550 ×  / 3.40 ×

diameter = 197.35 m

right

step-by-step explanation:

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)