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

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: