Cloud Observatory and Astronomy

Sunday, 11 September 2011

Distances, Magnitudes and Spectral Classes Equations

m = -2.5 log I + constant

d = R / tan θ_p (d = Distance (m))

θ_p = (t / 3600)°

θ = 2θ_p = W / d (d = Distance (m))

m_b - m_a = 2.5 log (L_a/ L_b)

m - M = 5 log (d / 10) (d = Distance (parsecs))

R (Radius of Earth Orbit and 1 Astronomical Unit (AU)) = 1.5x10¹¹ m

W (Width of Earth Orbit) = 3x10¹¹ m

1 pc = 3.09x10¹⁶ m

1 Mpc = 3.09x10²²m

m, m_a, m_b (Apparent Magnitude)

I (Intensity) = W m^-2

θ_p (Angle of Parallax) = degrees

t (Time of Parallax) = s

L_a,L_b (Luminosity) = W

M (Absolute Magnitude)

Monday, 5 September 2011

Lenses and Telescopes Equations

P = 1 / f

1 / f = 1 / u + 1 / v (Convex Lens)

1 / f = 1 / v - 1 / u (Concave Lens)

M = θ_i / θ_o = f_o / f_e = β / α

α = h / f_o

β = h / f_e

θ ≈ λ / D

f = f_o + f_e

s = r θ

P (Power) = D (Dioptres)

f (Focal Length) = cm

u (Object Distance) = cm

v (Image Distance) = cm

M (Magnification)

θ_i (Image Angle) = Degrees

θ_o (Object Angle) = Degrees

f_o (Objective Lens Focal Length) = cm

f_e (Eyepiece Lens Focal Length) = cm

β (Angle Subtended at Eye Using Instrument) = Radians

α (Angle Subtended at Unaided Eye) = Radians

h (Height of Object) = cm

θ (Angular Resolution) = Radians

λ (Wavelength) = m

D (Aperture) = m

r (Radius) = m

s (Distance) = m

Sunday, 28 August 2011

Ray Diagrams and Telescopes

The rays parallel to the principal axis are converged onto the principal focus.

The focal length is the distance between the lens axis and the principal focus.

Thicker lenses bend light more, and are therefore described as more powerful.

Powerful lenses have short focal lengths.

Rules for Ray Diagrams

1) Any incident ray travelling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.

2) Any incident ray travelling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.

3) Any incident ray which passes through the centre of the lens will in effect continue in the same direction that it had when it entered the lens.

Positive Image Distance	Negative Image Distance
Real	Virtual
Inverted	Upright
Erect (More Positive than Focal Length) Diminished (Less Positive than Focal Length)	Erect (More Negative than Focal Length) Diminished (Less Negative than Focal Length)

Refracting Telescope

A simple telescope is made of 2 converging lenses.

One is the objective lens of long focal length

One is the eyepiece of short focal length

Concave Reflecting Telescope

In a reflecting telescope, a large concave mirror is used as the objective, instead of a lens.

Parabolic Reflecting Telescope

Parabolic reflectors are used to collect energy from a distant source and bring it to a common focal point, thus correcting spherical aberration found in simpler reflectors.

Cassegrain Reflecting Telescope

The Cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and radio antennas.

In a symmetrical Cassegrain, both mirrors are aligned about the optical axis, and the primary mirror usually contains a hole in the centre thus permitting the light to reach an eyepiece.