Astronomy Quiz: Telescope Types
20 questions · exam conditions
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Telescope TypesQuestion 1 of 20

A major challenge for large, ground-based reflecting telescopes is atmospheric turbulence ('seeing'), which often limits the effective resolution to ~1 arcsecond, regardless of the telescope's theoretical diffraction limit. High-quality apochromatic refractors with apertures around 15 cm have a theoretical resolution of ~0.8 arcseconds. What does this imply about their relative performance on a typical night?

The refractor will always outperform the large reflector because its theoretical resolution is better than the seeing limit.
The refractor will produce sharper images because it is less affected by atmospheric turbulence due to its smaller aperture.
Both telescopes will produce images with the same level of detail, as the atmosphere is the limiting factor for both.
The reflector's large aperture will still allow it to see much fainter objects, even though its resolution is limited by the atmosphere.
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Astronomy Quiz

Astronomy Quiz: Telescope Types

Practice Telescope Types in Astronomy with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Telescope Types, giving you a quick way to practice the rules, question types, and explanations that matter most for Astronomy.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A major challenge for large, ground-based reflecting telescopes is atmospheric turbulence ('seeing'), which often limits the effective resolution to ~1 arcsecond, regardless of the telescope's theoretical diffraction limit. High-quality apochromatic refractors with apertures around 15 cm have a theoretical resolution of ~0.8 arcseconds. What does this imply about their relative performance on a typical night?

  1. The refractor will always outperform the large reflector because its theoretical resolution is better than the seeing limit.
  2. The refractor will produce sharper images because it is less affected by atmospheric turbulence due to its smaller aperture.
  3. Both telescopes will produce images with the same level of detail, as the atmosphere is the limiting factor for both.
  4. The reflector's large aperture will still allow it to see much fainter objects, even though its resolution is limited by the atmosphere. (correct answer)
Explanation: When you encounter telescope performance questions, you need to distinguish between two key factors: resolution (ability to see fine detail) and light-gathering power (ability to detect faint objects). These are fundamentally different capabilities that depend on different physical principles. Under typical seeing conditions, atmospheric turbulence blurs starlight to about 1 arcsecond, regardless of telescope size. This means that once a telescope's theoretical resolution is better than the seeing limit, further improvements in optical quality won't enhance detail visibility—the atmosphere becomes the bottleneck. Both the large reflector and the 15 cm refractor are limited to ~1 arcsecond resolution by atmospheric seeing. However, light-gathering power depends entirely on aperture area. A large reflector with, say, a 4-meter aperture collects over 700 times more light than a 15 cm refractor. This dramatically superior light-gathering ability allows detection of much fainter objects, even when atmospheric seeing prevents either telescope from achieving its theoretical resolution limit. Answer A is wrong because having better theoretical resolution than the seeing limit provides no practical advantage—the atmosphere still limits both telescopes equally. Answer B incorrectly suggests smaller apertures are less affected by turbulence; atmospheric seeing affects all ground-based telescopes similarly. Answer C correctly identifies that resolution is atmosphere-limited for both, but misses that light-gathering power differs dramatically. Remember: when atmospheric seeing is the limiting factor, compare telescopes based on light-gathering power (aperture area), not theoretical resolution. Bigger apertures always win for detecting faint objects.

Question 2

A Cassegrain reflecting telescope uses a concave primary mirror and a convex secondary mirror. An amateur astronomer incorrectly claims that the main purpose of the convex secondary mirror is to correct for the primary mirror's inherent chromatic aberration. Why is this reasoning flawed?

  1. Only lenses, not mirrors, suffer from chromatic aberration, as reflection is independent of wavelength. (correct answer)
  2. The secondary mirror in a Cassegrain design is actually flat and only serves to redirect the light path.
  3. Chromatic aberration is corrected by the eyepiece, not by any of the telescope's main mirrors.
  4. The convex secondary mirror is designed to correct for spherical aberration, not chromatic aberration.
Explanation: The correct answer is A. The fundamental flaw in the reasoning is that mirrors do not produce chromatic aberration. This aberration is caused by dispersion, the phenomenon where the refractive index of a material (like glass) varies with the wavelength of light. Since mirrors work by reflection, and the law of reflection (angle of incidence equals angle of reflection) is the same for all wavelengths, mirrors bring all colors of light to the same focus naturally. The secondary mirror's purpose is to fold the light path and increase the effective focal length, not to correct for an aberration that doesn't exist in a reflector.

Question 3

The theoretical angular resolution of a telescope is given by θ≈1.22λ/D\theta \approx 1.22 \lambda / D. A telescope with a 2-meter aperture is observing a celestial object in visible light (λ\lambda = 500 nm). An astronomer wants to achieve the same theoretical angular resolution while observing in the mid-infrared (λ\lambda = 5000 nm). What aperture diameter would a new telescope need for this infrared observation?

  1. 0.2 meters
  2. 2 meters
  3. 10 meters
  4. 20 meters (correct answer)
Explanation: The correct answer is D. The goal is to keep the angular resolution θ\theta constant. The initial resolution is θ1∝λ1/D1\theta_1 \propto \lambda_1 / D_1. The new resolution is θ2∝λ2/D2\theta_2 \propto \lambda_2 / D_2. For θ1=θ2\theta_1 = \theta_2, we must have λ1/D1=λ2/D2\lambda_1 / D_1 = \lambda_2 / D_2. We are given D1=2D_1 = 2 m, λ1=500\lambda_1 = 500 nm, and λ2=5000\lambda_2 = 5000 nm. The wavelength is increasing by a factor of 5000/500=105000/500 = 10. To keep the ratio constant, the aperture D2D_2 must also increase by a factor of 10. Therefore, the new aperture must be D2=D1×10=2 m×10=20D_2 = D_1 \times 10 = 2 \text{ m} \times 10 = 20 meters.

Question 4

An astronomer wishes to resolve a close binary star system with an angular separation of 0.15 arcseconds. Telescope A is a 15-cm apochromatic refractor, and Telescope B is a 40-cm Newtonian reflector. Assuming both telescopes are of perfect optical quality and observations are made from space (i.e., limited only by diffraction), which statement best describes their performance for this task?

  1. Telescope A is more suitable because its unobstructed aperture provides higher image contrast, which is the most critical factor for splitting close binary stars.
  2. Telescope B will resolve the binary system while Telescope A will not, because its larger aperture provides superior angular resolution. (correct answer)
  3. Both telescopes will resolve the binary system equally well, as the specified separation is well within the capabilities of any high-quality amateur instrument.
  4. Neither telescope can resolve the system, as resolving features smaller than 0.5 arcseconds requires an aperture of at least 1 meter in diameter.
Explanation: The correct answer is B. The theoretical angular resolution of a telescope is determined by the Rayleigh criterion, θ≈1.22λ/D\theta \approx 1.22 \lambda / D, where DD is the aperture diameter. A larger aperture results in a smaller diffraction limit (better resolution). Telescope B has a much larger aperture (40 cm) than Telescope A (15 cm), giving it significantly better theoretical resolution. While Telescope A may have higher contrast due to its lack of a central obstruction, this cannot overcome the fundamental diffraction limit imposed by its smaller aperture. Telescope B's superior resolution is the deciding factor for this specific task.

Question 5

An engineering team is designing a large-aperture space telescope for imaging faint, distant galaxies across a wide range of wavelengths, from ultraviolet to near-infrared. Why is a reflecting design, such as a Ritchey-Chrétien, universally chosen over a refracting design for such a mission?

  1. Reflectors can be designed with shorter focal lengths than refractors of the same aperture, making the telescope more compact and structurally stable for launch.
  2. Reflecting telescopes are immune to spherical aberration, which is the primary optical flaw that limits the performance of large-aperture refractors.
  3. The primary mirror of a reflector can be made significantly larger and lighter than a lens, and it does not suffer from chromatic aberration. (correct answer)
  4. Lenses for refracting telescopes cannot be given anti-reflection coatings for space applications, leading to significant light loss compared to a reflector's mirror.
Explanation: The correct answer is C. Large professional telescopes, especially space telescopes, are reflectors for two primary reasons. First, mirrors can be supported from behind, allowing for very large, yet relatively thin and lightweight, structures. A large lens (as in a refractor) can only be supported at its edges and will sag under its own weight, distorting the image. This is a critical engineering constraint that limits refractors to about 1 meter in diameter. Second, mirrors reflect all wavelengths of light at the same angle, so they do not suffer from chromatic aberration, where a lens focuses different colors at different points. This is essential for a telescope designed to observe across a wide spectral range.

Question 6

An astronomer compares the performance of a 4-meter telescope to a newly commissioned 8-meter telescope of the same design. Assuming both are observing the same faint object and are limited by diffraction, by what factors have the light-gathering power and theoretical angular resolution improved with the larger telescope?

  1. Light-gathering power is 2 times greater; resolution is 2 times better.
  2. Light-gathering power is 4 times greater; resolution is 2 times better. (correct answer)
  3. Light-gathering power is 2 times greater; resolution is 4 times better.
  4. Light-gathering power is 4 times greater; resolution is 4 times better.
Explanation: The correct answer is B. Light-gathering power is proportional to the area of the primary optic, which is proportional to the square of its diameter (A∝D2A \propto D^2). Doubling the diameter from 4 m to 8 m increases the light-gathering power by a factor of 22=42^2 = 4. Theoretical angular resolution is inversely proportional to the diameter (θ∝1/D\theta \propto 1/D). Doubling the diameter improves the resolution (makes the smallest resolvable angle smaller) by a factor of 2.

Question 7

An observer notes that images of bright stars viewed through a simple refractor have distinct violet-colored halos. An upgrade to an apochromatic (APO) refractor of the same aperture eliminates this issue. What is the primary trade-off associated with this upgrade?

  1. A significant increase in cost and complexity due to the use of multiple, exotic glass elements in the objective lens. (correct answer)
  2. A reduction in light-gathering power because the additional lens elements in the APO design absorb more light.
  3. An introduction of coma, an off-axis aberration, which is a common side effect of correcting for chromatic aberration.
  4. A longer cool-down time for the telescope, as the more massive APO lens takes more time to reach thermal equilibrium with the ambient air.
Explanation: The correct answer is A. The violet halos are a result of chromatic aberration, where a simple lens fails to bring all colors of light to the same focal point. An apochromatic (APO) refractor corrects this by using an objective lens made of three or more elements, often including expensive, exotic glasses with special dispersion properties. The primary trade-off for this near-perfect color correction is a dramatic increase in the cost and manufacturing complexity of the objective lens compared to a standard achromatic refractor or a reflector of the same aperture.

Question 8

Which of the following statements most accurately describes the relationship between a telescope's aperture and its performance for visual astronomy?

  1. Increasing aperture improves light-gathering power, but beyond a certain point it degrades resolution due to increased atmospheric distortion.
  2. For refracting telescopes, increasing aperture improves resolution but decreases light-gathering power due to increased glass absorption.
  3. Aperture size is primarily related to the maximum useful magnification of a telescope; a larger aperture allows for higher powers to be used effectively.
  4. A larger aperture increases both light-gathering power and theoretical resolution, allowing the observation of fainter objects with finer detail. (correct answer)
Explanation: When evaluating telescope performance, you need to understand how aperture (the diameter of the primary mirror or lens) affects the two fundamental capabilities: light-gathering power and resolution. A larger aperture dramatically improves light-gathering power because the area of the collecting surface increases with the square of the diameter. Double the aperture, and you collect four times more light, allowing you to see much fainter objects. Simultaneously, a larger aperture provides better theoretical resolution - the ability to distinguish fine details and separate close objects. This follows the Rayleigh criterion, where resolution improves (smaller angles) as aperture increases. Answer D correctly captures both these relationships: larger apertures increase light-gathering power AND theoretical resolution, enabling observation of both fainter objects and finer detail. Answer A incorrectly suggests that large apertures degrade resolution due to atmospheric effects. While Earth's atmosphere does limit practical resolution (called "seeing"), this doesn't change the telescope's theoretical resolving power - it's an external limitation, not an inherent aperture problem. Answer B falsely claims that larger refracting telescopes decrease light-gathering power due to glass absorption. While thick glass does absorb some light, the massive increase in collecting area far outweighs any absorption losses. Answer C confuses aperture's role with magnification. While larger apertures can support higher useful magnifications before images become too dim, aperture's primary benefits are light-gathering and resolution, not magnification itself. Remember: bigger aperture = more light + better resolution. These are the two fundamental advantages that drive telescope performance in visual astronomy.

Question 9

A Newtonian reflector with a high-quality parabolic primary mirror is advertised as being 'diffraction limited'. While this indicates it is free from spherical aberration on-axis, what is a different, significant optical aberration that will still be present, becoming more pronounced for objects away from the center of the field of view?

  1. Chromatic aberration
  2. Coma (correct answer)
  3. Lens sag
  4. Secondary spectrum
Explanation: The correct answer is B. Newtonian reflectors, even with perfect parabolic mirrors that eliminate on-axis spherical aberration, inherently suffer from an off-axis aberration called coma. Coma causes stars away from the center of the field of view to appear distorted, resembling small comets with their tails pointing away from the center. This is a primary limitation of the simple Newtonian design for wide-field imaging. Chromatic aberration and secondary spectrum are issues for refractors, and lens sag is a structural problem for large lenses.

Question 10

A Newtonian reflector with a high-quality parabolic primary mirror is advertised as being 'diffraction limited'. While this indicates it is free from spherical aberration on-axis, what is a different, significant optical aberration that will still be present, becoming more pronounced for objects away from the center of the field of view?

  1. Chromatic aberration
  2. Coma (correct answer)
  3. Lens sag
  4. Secondary spectrum
Explanation: The correct answer is B. Newtonian reflectors, even with perfect parabolic mirrors that eliminate on-axis spherical aberration, inherently suffer from an off-axis aberration called coma. Coma causes stars away from the center of the field of view to appear distorted, resembling small comets with their tails pointing away from the center. This is a primary limitation of the simple Newtonian design for wide-field imaging. Chromatic aberration and secondary spectrum are issues for refractors, and lens sag is a structural problem for large lenses.

Question 11

An observer notes that images of bright stars viewed through a simple refractor have distinct violet-colored halos. An upgrade to an apochromatic (APO) refractor of the same aperture eliminates this issue. What is the primary trade-off associated with this upgrade?

  1. A significant increase in cost and complexity due to the use of multiple, exotic glass elements in the objective lens. (correct answer)
  2. A reduction in light-gathering power because the additional lens elements in the APO design absorb more light.
  3. An introduction of coma, an off-axis aberration, which is a common side effect of correcting for chromatic aberration.
  4. A longer cool-down time for the telescope, as the more massive APO lens takes more time to reach thermal equilibrium with the ambient air.
Explanation: The correct answer is A. The violet halos are a result of chromatic aberration, where a simple lens fails to bring all colors of light to the same focal point. An apochromatic (APO) refractor corrects this by using an objective lens made of three or more elements, often including expensive, exotic glasses with special dispersion properties. The primary trade-off for this near-perfect color correction is a dramatic increase in the cost and manufacturing complexity of the objective lens compared to a standard achromatic refractor or a reflector of the same aperture.

Question 12

An astronomer is conducting a photometric study of a star in the ultraviolet (UV) portion of the spectrum, around 350 nanometers. Why would a large ground-based reflecting telescope be overwhelmingly preferred over a refracting telescope of the same aperture for this specific research?

  1. Refractors cannot be focused for UV light because the focal length of a lens is fixed for visible wavelengths.
  2. Standard optical glass used in refractor lenses is largely opaque to ultraviolet radiation, absorbing most of the light before it reaches the detector. (correct answer)
  3. Chromatic aberration is most severe in the UV spectrum, making it impossible for a refractor to produce a sharp image at these wavelengths.
  4. Reflecting telescopes naturally have a higher resolving power in the UV due to the shorter wavelength, whereas refractors do not gain resolution.
Explanation: The correct answer is B. A primary advantage of reflecting telescopes is that mirrors reflect all wavelengths of light, from UV to infrared, in the same way. In contrast, the glass used to make lenses for refracting telescopes absorbs a significant amount of light, especially at shorter wavelengths. Standard optical glass is largely opaque to UV light, meaning very little of the star's UV radiation would actually pass through the objective lens to be measured. This makes refractors unsuitable for most UV astronomy.

Question 13

A Cassegrain reflecting telescope uses a concave primary mirror and a convex secondary mirror. An amateur astronomer incorrectly claims that the main purpose of the convex secondary mirror is to correct for the primary mirror's inherent chromatic aberration. Why is this reasoning flawed?

  1. Only lenses, not mirrors, suffer from chromatic aberration, as reflection is independent of wavelength. (correct answer)
  2. The secondary mirror in a Cassegrain design is actually flat and only serves to redirect the light path.
  3. Chromatic aberration is corrected by the eyepiece, not by any of the telescope's main mirrors.
  4. The convex secondary mirror is designed to correct for spherical aberration, not chromatic aberration.
Explanation: The correct answer is A. The fundamental flaw in the reasoning is that mirrors do not produce chromatic aberration. This aberration is caused by dispersion, the phenomenon where the refractive index of a material (like glass) varies with the wavelength of light. Since mirrors work by reflection, and the law of reflection (angle of incidence equals angle of reflection) is the same for all wavelengths, mirrors bring all colors of light to the same focus naturally. The secondary mirror's purpose is to fold the light path and increase the effective focal length, not to correct for an aberration that doesn't exist in a reflector.

Question 14

Which of the following statements most accurately describes the relationship between a telescope's aperture and its performance for visual astronomy?

  1. Increasing aperture improves light-gathering power, but beyond a certain point it degrades resolution due to increased atmospheric distortion.
  2. For refracting telescopes, increasing aperture improves resolution but decreases light-gathering power due to increased glass absorption.
  3. Aperture size is primarily related to the maximum useful magnification of a telescope; a larger aperture allows for higher powers to be used effectively.
  4. A larger aperture increases both light-gathering power and theoretical resolution, allowing the observation of fainter objects with finer detail. (correct answer)
Explanation: When evaluating telescope performance, you need to understand how aperture (the diameter of the primary mirror or lens) affects the two fundamental capabilities: light-gathering power and resolution. A larger aperture dramatically improves light-gathering power because the area of the collecting surface increases with the square of the diameter. Double the aperture, and you collect four times more light, allowing you to see much fainter objects. Simultaneously, a larger aperture provides better theoretical resolution - the ability to distinguish fine details and separate close objects. This follows the Rayleigh criterion, where resolution improves (smaller angles) as aperture increases. Answer D correctly captures both these relationships: larger apertures increase light-gathering power AND theoretical resolution, enabling observation of both fainter objects and finer detail. Answer A incorrectly suggests that large apertures degrade resolution due to atmospheric effects. While Earth's atmosphere does limit practical resolution (called "seeing"), this doesn't change the telescope's theoretical resolving power - it's an external limitation, not an inherent aperture problem. Answer B falsely claims that larger refracting telescopes decrease light-gathering power due to glass absorption. While thick glass does absorb some light, the massive increase in collecting area far outweighs any absorption losses. Answer C confuses aperture's role with magnification. While larger apertures can support higher useful magnifications before images become too dim, aperture's primary benefits are light-gathering and resolution, not magnification itself. Remember: bigger aperture = more light + better resolution. These are the two fundamental advantages that drive telescope performance in visual astronomy.

Question 15

An astronomer is conducting a photometric study of a star in the ultraviolet (UV) portion of the spectrum, around 350 nanometers. Why would a large ground-based reflecting telescope be overwhelmingly preferred over a refracting telescope of the same aperture for this specific research?

  1. Refractors cannot be focused for UV light because the focal length of a lens is fixed for visible wavelengths.
  2. Standard optical glass used in refractor lenses is largely opaque to ultraviolet radiation, absorbing most of the light before it reaches the detector. (correct answer)
  3. Chromatic aberration is most severe in the UV spectrum, making it impossible for a refractor to produce a sharp image at these wavelengths.
  4. Reflecting telescopes naturally have a higher resolving power in the UV due to the shorter wavelength, whereas refractors do not gain resolution.
Explanation: The correct answer is B. A primary advantage of reflecting telescopes is that mirrors reflect all wavelengths of light, from UV to infrared, in the same way. In contrast, the glass used to make lenses for refracting telescopes absorbs a significant amount of light, especially at shorter wavelengths. Standard optical glass is largely opaque to UV light, meaning very little of the star's UV radiation would actually pass through the objective lens to be measured. This makes refractors unsuitable for most UV astronomy.

Question 16

A student argues that a 10-cm refractor is superior to a 10-cm reflector for all types of astronomical observation because the refractor's lens transmits nearly 100% of incoming light, while the reflector's two mirrors and central obstruction cause significant light loss. What is the primary flaw in this argument?

  1. The student overestimates the light loss in a reflector; modern mirror coatings are highly efficient, and the obstruction is minimal, leading to comparable light throughput.
  2. The student ignores the fact that reflectors do not suffer from chromatic aberration, which is a more significant image-degrading factor in refractors.
  3. The student's premise is incorrect; lenses inherently absorb some light and have surface reflections, resulting in a total light transmission that is often less than a reflector's. (correct answer)
  4. The student confuses light transmission with resolution; while the refractor may transmit more light, the reflector will always have better resolution due to its design.
Explanation: The correct answer is C. The student's core premise that a lens transmits nearly 100% of light is incorrect. Every time light passes through a surface (air-to-glass or glass-to-air), some is reflected. Even with anti-reflection coatings, this loss is typically a few percent per surface. Furthermore, the glass itself absorbs a small amount of light. A standard achromatic refractor has at least four surfaces. A modern reflector with a primary and secondary mirror can have a total reflectivity of over 90%. It is very common for a reflector to have a higher total light throughput than a refractor of the same aperture, directly contradicting the student's argument.

Question 17

All modern, large research telescopes with apertures greater than 2 meters are reflectors, not refractors. What is the fundamental physical limitation that prevents the construction of extremely large-aperture refracting telescopes?

  1. Chromatic aberration becomes non-correctable in lenses with diameters larger than approximately 1 meter, regardless of the glass type.
  2. A large glass lens can only be supported by its rim, and beyond a certain size, it will deform under its own weight, ruining image quality. (correct answer)
  3. The amount of light absorbed by the glass in a large lens becomes so great that it gathers less light than a smaller reflecting telescope.
  4. The polishing process for large lenses induces internal stresses that cause them to fracture easily during temperature changes.
Explanation: The correct answer is B. The primary engineering obstacle to building very large refractors is mechanical support. A lens must be transparent, so it can only be held in place by its edges. As a lens gets larger and more massive, gravity will cause it to sag and deform, altering its precise optical shape and destroying its ability to form a sharp image. In contrast, a mirror can be supported across its entire back surface with a complex support system, allowing for the construction of mirrors many meters in diameter.

Question 18

A student looking at specifications for two telescopes sees that both have the same aperture size. Telescope R is a refractor, and Telescope N is a Newtonian reflector. For a given eyepiece, Telescope R produces a much higher magnification. What does this imply about the primary optics of the two telescopes?

  1. Telescope R's objective lens has a longer focal length than Telescope N's primary mirror. (correct answer)
  2. Telescope R's objective lens is of higher optical quality, allowing for more useful magnification.
  3. Telescope N's secondary mirror reduces the effective magnification of the system.
  4. Telescope N must have a larger f-ratio than Telescope R.
Explanation: The correct answer is A. Magnification is calculated as the focal length of the telescope's primary optic divided by the focal length of the eyepiece (M=fobjective/feyepieceM = f_{objective} / f_{eyepiece}). Since the aperture and eyepiece are the same, the only way for Telescope R to produce a higher magnification is if its objective lens has a longer focal length than Telescope N's primary mirror. While optical quality (B) affects how well high magnification can be used, it does not determine the magnification itself. Focal length is the key parameter here.

Question 19

The theoretical angular resolution of a telescope is given by θ≈1.22λ/D\theta \approx 1.22 \lambda / D. A telescope with a 2-meter aperture is observing a celestial object in visible light (λ\lambda = 500 nm). An astronomer wants to achieve the same theoretical angular resolution while observing in the mid-infrared (λ\lambda = 5000 nm). What aperture diameter would a new telescope need for this infrared observation?

  1. 0.2 meters
  2. 2 meters
  3. 10 meters
  4. 20 meters (correct answer)
Explanation: The correct answer is D. The goal is to keep the angular resolution θ\theta constant. The initial resolution is θ1∝λ1/D1\theta_1 \propto \lambda_1 / D_1. The new resolution is θ2∝λ2/D2\theta_2 \propto \lambda_2 / D_2. For θ1=θ2\theta_1 = \theta_2, we must have λ1/D1=λ2/D2\lambda_1 / D_1 = \lambda_2 / D_2. We are given D1=2D_1 = 2 m, λ1=500\lambda_1 = 500 nm, and λ2=5000\lambda_2 = 5000 nm. The wavelength is increasing by a factor of 5000/500=105000/500 = 10. To keep the ratio constant, the aperture D2D_2 must also increase by a factor of 10. Therefore, the new aperture must be D2=D1×10=2 m×10=20D_2 = D_1 \times 10 = 2 \text{ m} \times 10 = 20 meters.

Question 20

A telescope's theoretical resolution improves when observing in bluer (shorter wavelength) light. If a 1-meter telescope can just resolve two stars separated by 0.14 arcseconds in red light (λ\lambda = 700 nm), what is the approximate angular separation of two stars it could just resolve in blue-violet light (λ\lambda = 400 nm)?

  1. 0.08 arcseconds (correct answer)
  2. 0.14 arcseconds
  3. 0.25 arcseconds
  4. 0.49 arcseconds
Explanation: The correct answer is A. The angular resolution θ\theta is directly proportional to the wavelength λ\lambda (θ∝λ\theta \propto \lambda). We can set up a ratio: θblue/θred=λblue/λred\theta_{blue} / \theta_{red} = \lambda_{blue} / \lambda_{red}. We are given θred=0.14\theta_{red} = 0.14 arcseconds, λred=700\lambda_{red} = 700 nm, and λblue=400\lambda_{blue} = 400 nm. Solving for θblue\theta_{blue}: θblue=θred×(λblue/λred)=0.14×(400/700)=0.14×(4/7)≈0.14×0.57=0.08\theta_{blue} = \theta_{red} \times (\lambda_{blue} / \lambda_{red}) = 0.14 \times (400 / 700) = 0.14 \times (4/7) \approx 0.14 \times 0.57 = 0.08 arcseconds. The resolution improves (the minimum resolvable angle gets smaller) at shorter wavelengths.