Question 1

A Cassegrain telescope has a primary mirror with a 5-m diameter and a hole of diameter 5 cm through the primary mirror. By what percent is the light-gathering power of the mirror reduced because of the hole?

Accepted Answer

The area of the hole is much smaller compared to the area of the primary mirror, resulting in a negligible reduction in light-gathering power.

Question 2

A refracting telescope has an objective lens of focal length 40 cm and a diameter of 10 cm, and an eyepiece of focal length 5 cm and diameter 1 cm. What is the magnifying power of this telescope?

Accepted Answer

The answer of A refracting telescope has an objective lens...

Question 3

A department store sells an "astronomical telescope" with an objective lens of 30-cm focal length and a diameter of 5 cm, and an eyepiece lens of focal length 5 mm and diameter 4 mm. What is the magnifying power of this telescope?

Accepted Answer

The magnifying power of a telescope is given by the formula: Magnifying Power = Focal Length of Objective Lens / Focal Length of Eyepiece Lens. Here, the focal length of the objective lens is 30 cm (or 300 mm) and the focal length of the eyepiece lens is 5 mm. Therefore, the magnifying power is 300 mm / 5 mm = 60×.

Question 4

In general, doubling the diameter of an optical telescope will

Accepted Answer

Doubling the diameter of an optical telescope quadruples its light-gathering power because the area (and thus the light-gathering power) is proportional to the square of the diameter. It also improves the angular resolution by a factor of 2, as the resolution is inversely proportional to the diameter.

Question 5

A small refracting "spyglass" telescope has an objective lens with a diameter of 2 inches. The world's largest refracting telescope at Yerkes Observatory has an objective lens with a diameter of 40 inches. Assuming that all light striking the objective lenses passes through them, how much larger is the light-gathering power of Yerkes than the spyglass?

Accepted Answer

The light-gathering power of a telescope is proportional to the area of its objective lens. The area of a circle (which is the shape of the lens) is given by πr^2, where r is the radius. Since the diameter is twice the radius, a lens with a diameter of 40 inches has a radius 20 times larger than a lens with a diameter of 2 inches. Because the area goes with the square of the radius, the Yerkes telescope gathers (20^2) = 400 times more light than the spyglass.

Question 6

By what factor is the light-gathering power of the 10-m diameter Keck telescope on Mauna Kea in Hawaii greater than an average unaided human eye, with a typical aperture diameter of 5 mm?

Accepted Answer

The answer of By what factor is the light-gathering power...

Question 7

The secondary mirror of a telescope whose primary mirror is 4 m in diameter has a diameter of 0.5 m. What fraction of the incoming light is obstructed by this secondary mirror?

Accepted Answer

The fraction of light obstructed is the area of the secondary mirror divided by the area of the primary mirror. The area of the secondary mirror is (0.5/4)^2 = 0.0625, which is 6.25% of the primary mirror's area.

Question 8

A small refracting "spyglass" telescope has an objective lens with a focal length of about 30 inches. The world's largest refracting telescope at Yerkes Observatory has an objective lens with a focal length of 63.5 feet. If they both use the same eyepiece, how much larger is the image with Yerkes than with the spyglass?

Accepted Answer

The magnification of a telescope is directly proportional to the focal length of the objective lens. The Yerkes telescope's focal length is 63.5 feet (or 762 inches), and the spyglass's focal length is 30 inches. Dividing 762 by 30 gives 25.4, which means the image with Yerkes is about 25 times larger than with the spyglass.

Question 9

How much more light can the 5-m telescope at Mount Palomar collect from an astronomical source than can the unaided human eye (with a diameter of 5 mm)?

Accepted Answer

The amount of light a telescope can collect compared to the human eye is proportional to the area of its aperture. The area of a circle (which is the shape of both the telescope's aperture and the pupil of the eye) is given by πr^2, where r is the radius of the circle. Since the diameter of the telescope is 5 m (or 5000 mm) and the diameter of the human eye is approximately 5 mm, the radius of the telescope's aperture is 2500 mm and the radius of the eye's pupil is 2.5 mm. Squaring these and taking the ratio gives (2500^2) / (2.5^2) = 1,000,000. Therefore, the 5-m telescope can collect 1,000,000 times more light than the unaided human eye.

Question 10

Which of these characteristics of an astronomical telescope is the MOST important for determining the angular resolution?

Accepted Answer

The diameter of the objective lens or mirror is the most important factor for determining the angular resolution of a telescope. A larger diameter allows the telescope to collect more light and resolve finer details, improving its ability to distinguish objects that are close together in the sky.

Question 11

How many times more light will be collected by the optics of one side of a pair of binoculars (7 × 50-magnification of 7 and an objective lens aperture diameter of 50 mm) than by an average human eye, with a typical aperture diameter of 5 mm?

Accepted Answer

The answer of How many times more light will be...

Question 12

How can one increase the magnification of a refracting telescope without decreasing the light-gathering power?

Accepted Answer

Decreasing the focal length of the eyepiece increases the magnification without affecting the light-gathering power, which is determined by the diameter of the objective lens.

Question 13

A particular reflecting telescope has a primary mirror 0.4 m in diameter and 4.0-m focal length and an eyepiece lens 1.0 cm in diameter and 2.0-cm focal length. What is the magnifying power of this telescope?

Accepted Answer

The magnifying power of a telescope is given by the ratio of the focal length of the primary mirror to the focal length of the eyepiece. Thus, magnifying power = (4.0 m / 0.02 m) = 200×.

Question 14

Many amateur astronomers have telescopes with mirrors 20 cm (1/5 m) in diameter. In comparison, one of the largest astronomical telescopes in the world is the Keck telescope, with a diameter of 10 m. How much greater is the light-gathering power of the Keck telescope than the power of a 20-cm telescope?

Accepted Answer

The light-gathering power of a telescope is proportional to the area of its mirror, which is calculated as πr^2. Comparing the areas (and thus the light-gathering powers) of the two telescopes, the ratio is (5^2) / (0.1^2) = 25^2 = 625. Since the question asks for how much greater, not the total amount, the correct answer is 625 times greater, which is not listed. However, the correct approach to calculate the light-gathering power difference involves comparing the diameters squared (since area ∝ diameter^2 for circles), leading to (10^2) / (0.2^2) = 100 / 0.04 = 2500 times greater.

Question 15

The angle between two adjacent stars whose images can just barely be distinguished by the telescope is a measure of the telescope's

Accepted Answer

The angle between two adjacent stars that can just barely be distinguished by a telescope is a measure of the telescope's resolution, which determines its ability to distinguish between two closely spaced objects.

Question 16

A particular reflecting telescope has an objective mirror with a focal length of 1.2 m and an eyepiece lens of focal length 6 mm. What is the magnifying power of this telescope?

Accepted Answer

The magnifying power of a telescope is given by the ratio of the focal length of the objective lens (or mirror) to the focal length of the eyepiece. Thus, magnifying power = 1.2 m / 6 mm = 1200 mm / 6 mm = 200×.

Question 17

What is the magnification of a Newtonian telescope that has a primary mirror of diameter 0.25 m and focal length of 2 m when used with an eyepiece of focal length 25 mm and an optical diameter of 5 mm?

Accepted Answer

The magnification of a telescope is given by the ratio of the focal length of the primary mirror (or lens) to the focal length of the eyepiece. Here, it is $ \frac{2000 \, \text{mm}}{25 \, \text{mm}} = 80 $ times.

Question 18

The BEST shape for the cross-section of a simple astronomical mirror in order to produce the sharpest images of very distant objects at its prime focus is a(n)

Accepted Answer

A parabolic shape is best for the cross-section of a simple astronomical mirror to produce the sharpest images of very distant objects at its prime focus because it focuses parallel rays of light (such as those coming from distant stars) to a single point, minimizing spherical aberration.

Question 19

For many years, the Palomar telescope (5-m diameter) in California was the largest telescope in the world; it has now been surpassed by a number of facilities, including both the Keck I and Keck II telescopes (each of diameter 10 m) in Hawaii. How much greater is the light-gathering power of a Keck telescope than that of the Palomar telescope?

Accepted Answer

The light-gathering power of a telescope is proportional to the area of its aperture, which is proportional to the square of its diameter. The Keck telescope has a diameter of 10 m, and the Palomar telescope has a diameter of 5 m. The ratio of their light-gathering powers is (10/5)^2 = 4.

Question 20

Compared with the 2.5-m diameter Mount Wilson telescope, each of the 10-m diameter Keck telescopes has a greater light-gathering power by a factor of

Accepted Answer

The light-gathering power of a telescope is proportional to the area of its mirror, which is proportional to the square of its diameter. Therefore, comparing the 10-m diameter Keck telescopes to the 2.5-m diameter Mount Wilson telescope, the factor increase in light-gathering power is (10/2.5)^2 = 4^2 = 16.

Quiz 3: Light and Telescopes