Optics and Light

• Astro 113-02 for the Winter of 2025, S.5

Topics

• Light, Reflection, Refraction
• Refracting Telescopes
• Reflecting Telescopes

Telescopes

• Telescopes are optical instruments used to observe distant objects by collecting and magnifying light.
• The two main types of telescopes are refracting and reflecting telescopes.
• These differ in how they gather and focus light.
• Refracting telescopes use lenses to bend (refract) light 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

• In a uniform medium, light travels in a straight line unless an obstacle or a change in medium alters its course.
• Light travels fastest in a vacuum at a speed of light c = 3.00 × 10⁸ m/s and slows down in denser materials like water or glass.

Reflection

• Reflection is the process by which a wave like light bounces off a surface.
• The Law of Reflection is that the Angle of Incidence = Angle of Reflection.

Refraction (The Bending of Light)

• Refraction is the bending of light as it passes from one medium to another with a different optical density.
• This occurs because light changes speed when moving between materials with different refractive indices.
• Refractive Index (n) measures how much light slows down in a medium.
• Example of refraction: A straw appearing bent in a glass of water.
• Example of refraction: Water in a pool appears shallower than its true depth due to the bending of light.
• Rainbows form when light refracts through raindrops.
• Refraction is mathematically described by Snell's Law: n₁sin(0₁) = n₂sin(0₂).
• n₁ and n₂ are the refractive indices of the two media.
• 0₁ is the angle of incidence or incoming light.
• 0₂ is the angle of refraction or bent light.
• In Snell's Law, the angles of incidence and refraction are relative to the normal line, is perpendicular to the boundary between the two media.
• The Normal Line is an imaginary perpendicular line at the boundary between two media, used to measure angles of incidence and refraction.
• The Refractive Index (n): n = c / v where c is the speed of light in a vacuum and v is the speed of light in the material.
• Vacuum refractive index: 1.00 (no refraction)
• Air refractive index: 1.0003
• Glass refractive index: 1.5
• Water refractive index: 1.33
• Diamond refractive index: 2.42
• Example Problem: 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.
• Answer: 1.0 × sin(30°) = n2 × sin(20°) becomes n2=1.0 × sin(30°)/sin(20°), results to n2 approximately 1.46

Refracting Telescopes

• Refracting telescopes use lenses, specially shaped glass pieces that bend parallel light rays to meet at a single focal point.
• The focal point is where the light rays meet.
• Focal length is the distance from the lens to the focal point, and is represented by the symbol f.
• When an object is far away light rays coming from it are nearly parallel by the time they reach the lens.
• As a result, the image of the object is formed at the focal point.
• If the object is an “extended object”, such as the moon, the light from different parts of it arrive at different angles.
• 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.
• To view the image, an additional lens, called an eyepiece, is typically needed.
• The eyepiece forms an image of the initial image created by the first objective lens.
• The eyepiece is placed a distance equal to its focal length away from the first image, allowing the light rays entering to your eye to become parallel again.
• The final image appears to be at an infinite distance.
• 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.
• Magnification is the ratio of the image size to the object size.
• Magnification = f Objective / f Eyepiece
• Example Problem: 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?
• Answers: A) Magnification = 120 / 4.0 = 30 and B) Magnification = 120 / 2.0 = 60.
• 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.
• 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.
• The area is proportional to the square of its diameter.
• Doubling the diameter of an objective lens will multiply the light gathered by a factor of 4.
• A fully dark adapted human eye has a pupil diameter of about 5 mm.
• The 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 / (5mm)² = (2000)² = 4 × 10⁶
• Suppose looking at the Moon through an astronomical telescope. Someone then blocks lower half of the objective lens of the telescope with their hand, the person will see the whole Moon appear dimmer than before.
• Disadvantages of using refracting telescopes include the high cost of grinding both sides of large-diameter lenses.
• Reduced stability, as the lens can only be supported at the rim is a disadvantage.
• Need for expensive, optical-quality glass, free from imperfections like bubbles is a disadvantage.
• Long telescope length causes balancing issues when a heavy instrument is mounted at the eyepiece end.
• The main issue with refracting telescopes is chromatic aberration.
• Chromatic aberration occurs because a lens refracts different colors of light at slightly different angles, which causes the image to blur.
• Correcting chromatic aberration by using compound lenses made of different types of glass which is costly and impractical for big lenses.

Reflecting Telescopes

• Reflecting telescopes use a mirror to form an image the same way as an objective lens of a refracting telescope.
• Isaac Newton built the first reflecting telescope.
• Mirrors focus all wavelengths of light at the same focal point which eliminates chromatic aberration.
• Reflecting telescopes use parabolic mirrors to focus parallel light rays.
• The main issue with reflecting telescopes is that the focal point lies in the path of the incoming light.
• The Newtonian type of reflecting telescope uses a mirror to reflect the image sideways to minimize the issue of the focal point lying in the path of incoming light.
• Other common designs for reflecting telescopes include the Prime Focus, Cassegrain Focus, and Coudé Focus.
• Prime Focus is only used for very large telescopes where light obstructed by a camera is small.
• Cassegrain Focus is the most common and its 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 thus they do not have to move with the telescope.
• Advantages of using reflecting telescopes include elimination of chromatic aberration since light reflects off a mirror instead of passing through glass.
• Only one side of the glass needs to be ground to the correct shape.
• Reflecting telescopes have greater stability since the mirror can be supported from the back.
• Cheaper-quality glass can be used as light doesn't pass through it.
• Reflecting telescopes have a more compact size, reducing balance problems.

Explore the behaviour of light including refraction and reflection. Understand light's interaction with mediums such as air, water, and glass. Learn about telescopes, refractive indexes, and the nature of light.