The resolution of a telescope is ultimately limited by the diameter of its objective lens or mirror. A typical amateur astronomer's telescope may have a 6.09 in diameter mirror. What is the minimum angular separation (in arc seconds) of two stars that can be resolved with a 6.09 in scope

 θ =  3.19  arc second

Explanation:

The resolution of a telescope is given by the rayleigh criterion, which establishes that two objects are separated if the principal maximum of diffraction of one of them coincides with the first minimum of diffraction of the second object, based on this the solution is given by the first diffraction minimum, the a slit is

        a sin θ = m λ

with m = 1

in the case of circular apertures the equation must be found in polar coordinates, therefore a numerical constant is introduced

        a sin θ = 1.22 λ

Angles are measured in radians and in these experiments they are small

        sin θ = θ

       θ= 1.22  λ  / a

in this case a = 6.09 in, the wavelength is wrong = 550 10⁻⁹ m which is the maximum resolution of the human eye

l

et's reduce the magnitudes to the SI system

        d = 6.09‘  2.54 10⁻-2 m / 1 inch = 15.4686 10-2 m

let's calculate

       θ = 1.22 550 10-9 / 15.468 10-2

       θ = 15.5 10⁻⁶ rad

       rad = 2.06 105 s

       θ = 15.5 10⁻⁶ rad  2.06 105s/ 1 rad

       θ =  3.19   s

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.