Worksheet: Telescopes

In this worksheet, we will practice calculating the imaging properties of reflecting, refracting, and compound optical systems used in telescopes.

Q1:

What is the angular magnification of a telescope that has a 100 cm-focal length objective and a 2.50 cm-focal length eyepiece?

  • A 3 6 𝑥
  • B 4 8 𝑥
  • C 4 4 𝑥
  • D 4 0 𝑥
  • E 5 0 𝑥

Q2:

A 7.5x binocular produces an angular magnification of 7 . 5 0 , acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a 75.0-cm focal length, what is the focal length of the eyepiece lenses?

Q3:

A large reflecting telescope has an objective mirror with a 10.0-m radius of curvature. What angular magnification does it produce when a 3.00 m-focal length eyepiece is used?

  • A 1 8 8 x
  • B 1 5 0 x
  • C 1 6 7 x
  • D 1 3 3 x
  • E 1 7 5 x

Q4:

A planet at a distance of 1 0 m from Earth is observed by a telescope that has a focal length of the eyepiece of 1 cm and a focal length of the objective of 1 cm. The planet is seen to subtend an angle of 1 0 rad at the eyepiece. What is the size of the planet?

  • A 9 × 1 0 m
  • B 4 × 1 0 m
  • C 1 × 1 0 m
  • D 2 × 1 0 m
  • E 6 × 1 0 m

Q5:

Two stars that are 1 0 9 km apart are viewed by a telescope and found to be separated by an angle of 1 0 5 radians . If the eyepiece of the telescope has a focal length of 1.5 cm and the objective has a focal length of 3 meters, how far away are the stars from the observer?

  • A 6 × 1 0 1 6 km
  • B 1 × 1 0 1 6 km
  • C 4 × 1 0 1 6 km
  • D 1 × 1 0 1 7 km
  • E 2 × 1 0 1 6 km

Q6:

A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in the direction opposite to the normal one and can then be projected onto a satellite or the Moon. This is done with a telescope, producing a 3.50 m diameter beam of 630 nm wavelength light.

What is the minimum angular spread of the beam produced?

  • A 2 . 3 6 × 1 0 rad
  • B 4 . 7 8 × 1 0 rad
  • C 2 . 2 0 × 1 0 rad
  • D 1 . 9 8 × 1 0 rad
  • E 3 . 3 5 × 1 0 rad

Neglecting atmospheric effects, find the size of the spot this beam would make on the Moon. Use a value of 4 . 0 0 × 1 0 m for the distance to the Moon.

Q7:

In a reflecting telescope, the objective is a concave mirror of radius of curvature 4.0 m and the eyepiece is a convex lens of focal length 6.0 cm. Find the apparent size of a 5.0 m tree at 20 km that you would perceive when looking through the telescope.

Q8:

What is the distance between the objective lens and eyepiece in a telescope that has a 100 cm focal length objective and a 4 cm focal length eyepiece needed to produce a final image very far from the observer, where vision is most relaxed?

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