Question

My telescope has an objective focal length of 0.955m & a diameter of 11cm.

1) what should the eye piece focal length be if i want a magnification of 196?
2) what is the rayleigh limit to this telescope when using a wavelength of 425nm?
3) what power will the eye piece have?

Answer 1

The eyepiece focal length for the desired magnification is 4.872mm, the Rayleigh limit for the telescope is 4.732 x 10^-6 radians, and the power of the eyepiece is 205.14 Diopters.

Step-by-step explanation:

The student's telescope has an objective focal length of 0.955m and a diameter of 11cm. To calculate the eyepiece focal length for a magnification of 196, we use the magnification formula for telescopes:

Magnification (M) = Focal length of objective (fo) / Focal length of eyepiece (fe)

Substituting the given values, we get:

196 = 0.955m / fe

Solving for fe gives us:

fe = 0.955m / 196

fe = 0.004872m or 4.872mm

The Rayleigh limit (θ) is given by the formula:

θ = 1.22 λ / D

where λ is the wavelength of light and D is the diameter of the telescope's objective lens.

For λ = 425nm and D = 11cm, we have:

θ = 1.22 × 425 × 10-9m / 0.11m = 4.732 x 10-6 radians

The eyepiece's power (Pe) is the reciprocal of its focal length in meters:

Pe = 1 / fe

Pe = 1 / 0.004872m = 205.14 Diopters