Refraction and Telescopes PDF

Astro 113-02 Winter 2025 S.5 Topics Light, Reflection, Refraction Refracting Telescopes Reflecting Telescopes Telescopes Telescopes are optical instruments designed to observe distant objects by collecting and magnifying light. The two main types are refracting telescopes and...

Astro 113-02 Winter 2025 S.5 Topics Light, Reflection, Refraction Refracting Telescopes Reflecting Telescopes Telescopes Telescopes are optical instruments designed to observe distant objects by collecting and magnifying light. The two main types are refracting telescopes and reflecting telescopes, which differ in how they gather and focus light. Refracting Telescopes use lenses to bend (refract) light and bring it to a focus. Early telescopes, like the ones Galileo used, were refracting telescopes Reflecting Telescopes use mirrors instead of lenses to reflect and focus light. Important properties of Light Light travels in a straight line: In a uniform medium, light moves in a straight path unless an obstacle or a change in medium alters its course. Speed of Light in Different Media: Light travels fastest in a vacuum (speed of light 𝑐 = 3.00 × 108 𝑚/𝑠) and slows down in denser materials like water or glass. Reflection Reflection is the process in which a wave (such as light, sounds, or water) bounces off a surface instead of passing through it. Law of Reflection: Angle of Incidence=Angle of Reflection https://www.britannica.com/science/light/Reflection-and-refraction Refraction (The Bending of Light) Refraction is the bending of light as it passes from one medium to another with a different optical density, such as from air to water. This occurs because light changes speed when moving between materials with different refractive indices. Refractive Index (n): A measure of how much light slows down in a medium. Refraction Example: A straw appearing bent in a glass of water Water in a pool appears shallower than its true depth due to the bending of light. Rainbows form when light refracts as it passes through raindrops. Refraction Refraction is mathematically described by Snell’s Law. Snell’s Law: n1 sin θ1 = n2 sin(θ2 ) In this equation: n1 and n2 are the refractive indices of the two media, θ1 is the angle of incidence (incoming light), θ2 is the angle of refraction (bent light). IMPORTANT NOTE: In Snell's Law, the angles of incidence and refraction are measured relative to the normal line, which is perpendicular to the boundary between the two media. Refraction The Normal Line is an imaginary perpendicular line at the boundary between two media, used to measure angles of incidence and refraction. https://www.sciencelearn.org.nz/resources/49-refraction-of-light Refraction Refractive Index (n): 𝑐 𝑛= 𝑣 𝑐 is the speed of light in a vacuum. 𝑣 is the speed of light in the material. Some refractive indices: Vacuum: 1.00 (no refraction) Air: 1.0003 Glass: 1.5 Water: 1.33 Diamond: 2.42 Example A beam of light passes from air (refractive index 𝑛1 = 1.0) into a glass material. The angle of incidence in air is 30∘. If the angle of refraction in the glass is 20∘ , calculate the refractive index of the glass. Example A beam of light passes from air (refractive index 𝑛1 = 1.0) into a glass material. The angle of incidence in air is 30∘. If the angle of refraction in the glass is 20∘ , calculate the refractive index of the glass. Using Snell’s Law: n1 sin θ1 = n2 sin(θ2 ) 1.0 × sin 30∘ = 𝑛2 × sin(20∘ ) sin 30∘ 𝑛2 =1.0 × sin(20∘ ) 𝑛2 is approximately 1.46 Note: The refractive index of the glass is approximately 1.46 Telescopes Refracting telescopes utilize lenses, which are specially shaped glass pieces designed to bend parallel light rays so they meet at a single point. This point is known as the focal point. The distance from the lens to the focal point is referred to as the focal length, typically represented by the symbol f. Telescopes When an object is far away, the light rays coming from it are nearly parallel by the time they reach the lens. This occurs when observing astronomical objects, as their distance is vast compared to the focal length. As a result, the image of the object is formed at the focal point. Telescopes If the object is an “extended object”, such as the moon, the light from different parts of it arrive at different angles. So the image of the different parts of the object form at different parts of a plane, known as the focal plane, which is at a distance f from the lens. This is where you would place the film or the CCD sensor of a digital camera if you wanted to capture an image of the object. Telescopes To view the image with your eye, you typically need an additional lens called an eyepiece. The eyepiece forms an image of the initial image created by the first lens, known as the objective lens. The eyepiece is placed a distance equal to its focal length away from the first image, allowing the light rays entering your eye to become parallel again. As a result, the final image appears to be at an infinite distance. Telescopes Note: If the focal length of the eyepiece is smaller than the focal length of the objective lens, then the final image is larger than the actual object. The ratio of the image size to the object size is referred to as magnification. 𝑓𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 Magnification = 𝑓𝐸𝑦𝑒𝑝𝑖𝑒𝑐𝑒 Example A small refracting telescope has an objective lens with a focal length of 120 cm. A) Calculate the magnification when using an eyepiece with a focal length of 4.0 cm. B) If the eyepiece is replaced with one that has a focal length of 2.0 cm, determine the new magnification. How does the image size compare to the one produced by the first eyepiece? Example A small refracting telescope has an objective lens with a focal length of 120 cm. A) Calculate the magnification when using an eyepiece with a focal length of 4.0 cm. B) If the eyepiece is replaced with one that has a focal length of 2.0 cm, determine the new magnification. How does the image size compare to the one produced by the first eyepiece? 𝑓𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 120 Sol.: A) Magnification = = = 30 𝑓𝐸𝑦𝑒𝑝𝑖𝑒𝑐𝑒 4.0 𝑓𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 120 B) Magnification = = = 60 𝑓𝐸𝑦𝑒𝑝𝑖𝑒𝑐𝑒 2.0 Telescopes Another key advantage of using a telescope is its ability to gather more light than the human eye. All the light from a star that passes through the objective lens contributes to the brightness of the observed image. Therefore, a telescope with a high light-gathering power can detect faint objects that would otherwise be invisible to the human eye. The light gathered by a telescope is proportional to the area of the objective lens. Note: The area is proportional to the square of its diameter. Example: Doubling the diameter of an objective lens will multiply the light gathered by a factor of 4. Example A fully dark adapted human eye has a pupil diameter of about 5 mm. Keck telescope in Hawaii uses a concave mirror with a diameter of 10 m to bring starlight to a focus. The light-gathering power of the Keck telescopes is greater than that of the human eye by a factor of 10000 𝑚𝑚 2 2 = 2000 = 4 × 106 5𝑚𝑚 2 Note: the units should be the same! Question Suppose you are looking at the Moon through an astronomical telescope. Someone then blocks the bottom half of the objective lens of the telescope with their hand. What will happen to the image of the Moon you see through the telescope? a. You will see only the bottom half of the Moon. b. You will see only the top half of the Moon. c. You will see the whole Moon but the image will be distorted. d. You will see the whole Moon but it will appear dimmer than before. e. You will not notice any change. Question Suppose you are looking at the Moon through an astronomical telescope. Someone then blocks the bottom half of the objective lens of the telescope with their hand. What will happen to the image of the Moon you see through the telescope? a. You will see only the bottom half of the Moon. b. You will see only the top half of the Moon. c. You will see the whole Moon but the image will be distorted. d. You will see the whole Moon but it will appear dimmer than before. e. You will not notice any change. Telescopes Some disadvantages of using refracting telescopes: High cost of grinding both sides of large-diameter lenses. Reduced stability, as the lens can only be supported at the rim. Need for expensive, optical-quality glass, free from imperfections like bubbles. Long telescope length, which causes balancing issues when a heavy instrument is mounted at the eyepiece end. Telescopes The main issue with refracting telescopes is chromatic aberration. This occurs because a lens refracts different colors of light at slightly different angles, causing the image to blur. While it is possible to correct chromatic aberration by using compound lenses made of different types of glass (as in camera lenses), this approach is costly and impractical for very large lenses. Telescopes Reflecting Telescope Isaac Newton built the first reflecting telescope. A reflecting telescope uses a mirror to form an image in much the same way as the objective lens of a refracting telescope. Mirrors focus all wavelengths of light at the same focal point, eliminating chromatic aberration. Reflecting telescopes use parabolic mirrors to focus parallel light rays. However, the main issue is that the focal point lies in the path of the incoming light. Telescopes To minimize this problem we can use a mirror to reflect the image sideways. This is the Newtonian type of reflecting telescope.  Telescopes There are several other common designs for reflecting telescopes. Prime Focus only used for very large telescopes where light obstructed by a camera is small. Cassegrain Focus Most common The convex secondary mirror effectively lengthens the Objective or Primary mirror focal length, thus increasing the overall magnification Coudé Focus allows large instruments to be mounted far from the telescope itself so they do not have to move with the telescope. Telescopes Advantages of using reflecting telescopes include: Elimination of chromatic aberration, as light reflects off a mirror instead of passing through glass. Only one side of the glass needs to be ground to the correct shape. Greater stability, since the mirror can be supported from the back. The ability to use cheaper-quality glass, as light doesn’t pass through it. A more compact size, reducing balance problems