Telescopes

Angular Resolution #

The angular resolution of a telescope is given by

Why do blue wavelengths look sharper in a telescope compared to red wavelengths?

• The angular resolution θ (clarity) of a telescope is given

  by θ = λ/D, where λ is the wavelength of light observed and D is the diameter of the

  mirror or lens of the telescope. Blue light has a shorter wavelength than red light,

  so for a given telescope size D, the value of θ is smaller for blue light than for red

  light. That means the angular resolution is better for blue light than for red light;

  the images will look sharper in blue light. For example, two stars very close together

  may be resolved (i.e., clearly separated from each other) when observed in blue light

  but blurred together when observed in red light.

Light Gathering Power #

How is a telescope’s size (radius) related to its strength (amount of light it can gather)?

• Light gathering power is directly proportional to area ($\pi r^2$).
• A telescope that’s twice as wide will have 4 times the power.

Types of Telescopes #

What are some types of telescopes and their issues?

• Space vs. Earth telescopes: space telescopes are much more expensive, but land-based telescopes suffer from atmospheric distortion which greatly reduces their clarity, especially at lower elevations and on windy days.
  • The atmosphere also blocks UV, X-rays, gamma rays, and infrared radiation (so space telescopes are necessary for viewing these wavelengths).
• Refracting telescopes focus light onto a single point using a glass lens. They are prone to chromatic aberration, the phenomenon where light entering a glass lens bends in different amounts based on its wavelength. Longer wavelengths (e.g. red) are bent less than shorter wavelengths (e.g. purple).
• Reflecting telescopes use mirrors to focus and redirect light. Imperfections in the mirror’s shape can cause light to focus at different points, which is known as spherical aberration. This was the issue the Hubble Space Telescope initially had due to a misshapen mirror.
• SCT (Schmidt-Cassegrain)

Twinkling #

Why do stars appear to twinkle?

• Stars twinkle because of the constant shifting of particles in the atmosphere: sometimes, they align in such a way to block more light coming from a star; in other times, there are fewer particles and so the star appears brighter.
• The light output of stars is not actually changing when twinkling is observed. Rather, the near-constant output is refracted in different ways by Earth’s atmosphere.

Parallax #

What is parallax? How can it be used to measure the distances of stars?

• The parallax effect can be observed when you close one eye, then close the other, and notice the shift of objects you’re looking at.
• In astronomy, parallax is the angle covered by 1 AU (distance from earth to sun).
  • $d = 1/p$, where $d$ is the distance in parsecs (3.26 light years, the distance for which 1 AU separation creates a 1 arcsecond shift) and $p$ is the parallax in arcseconds. 60 arcseconds make an arcminute, and 60 arcminutes make 1 degree. 360 degrees is a full circle.