19.2 Lenses - Grade 9 Physical Science Study Guide

Learning Objectives for Lenses

• Explain the underlying causes that lead light to undergo refraction when passing through different media.
• Provide a formal definition for the index of refraction as it relates to optical physics.
• Describe the specific physical characteristics that define concave and convex lenses.
• Distinguish between the different types of images (real vs. virtual) formed by concave and convex lenses.
• Describe the phenomenon of total internal reflection and explain its specific relationship to the critical angle.

The Mechanism of Refraction

• Light rays slow down and bend as they pass through curved glass lenses; in specific configurations, this results in the production of a magnified image.
• Light typically travels in straight lines.
• In a vacuum, light travels at a constant speed of approximately $3.00 \times 10^8\,m/s$.
• The speed of light in any medium other than a vacuum depends entirely on the material composition of that new medium.
• Air allows light to pass through at a velocity almost as fast as its speed through a vacuum.
• Specific Speeds of Light in Different Media:     - In water, the speed of light is $2.25 \times 10^8\,m/s$.     - In glass, the speed of light is $2.00 \times 10^8\,m/s$.
• Speed Changes and Bending:     - When light passes from air into a denser medium like glass or water, it slows down.     - When light passes from glass or water back into air, it speeds up.     - Refraction is caused when light enters a new medium at an angle; the resulting change in speed causes the light to bend.
• A light ray refracts as it passes through media with different indices of refraction. However, the ray will travel in its original direction once it reenters the air, regardless of the refraction that occurred while it was within water or glass layers.

The Index of Refraction

• The total amount of refraction is dependent upon the difference between the speeds of light in the two adjacent media.
• The mathematical definition for the index of refraction of a material is the ratio of the speed of light in a vacuum to the speed of light within that material.
• Indices Comparisons:     - A low index of refraction (near the value of $1$) causes light to slow and refract very little.     - Diamond has a high index of refraction of $2.42$, which causes significant refraction.

Properties of Gemstones

• Gemstones are recognized for physical properties including luster and optical brilliance.
• Luster: This is a measure of the amount of light that strikes the surface of a gemstone and is reflected. Luster is increased by flat and smooth surfaces.
• Brilliance: While luster involves surface reflection, brilliance involves the light that passes into the stone. Brilliance is a measure of the amount of light entering the gem that is then reflected back to the viewer.
• Precise cutting techniques are utilized to shape gemstones to produce maximum brilliance. The intensity of brilliance is a combination of the specialized shape and the inherent high index of refraction of the gemstone.
• Comparative Material Table (Index of Refraction and Luster):     - Moissanite (manufactured diamond simulant): Highly lustrous at $20.4\%$.     - Emerald: The least lustrous in the provided data set at $4.8\%$.
• Calculation Example for Gemstone Identification:     - Question: The speed of light through an unknown gemstone is $1.69 \times 10^8\,m/s$. Identify the gemstone.     - Formula: $\text{Index of refraction} = \frac{\text{speed of light in vacuum}}{\text{speed of light in gemstone}}$     - Calculation: $\frac{3.00 \times 10^8\,m/s}{1.69 \times 10^8\,m/s} = 1.77$     - Conclusion: Based on an index of $1.77$, the gemstone could be identified as either a ruby or a sapphire.

Concave Lenses

• A lens is defined as an object made of transparent material featuring one or two curved surfaces used to refract light.
• Physical Characteristics: A concave lens is curved inward at the center and is thickest at its outside edges.
• Ray Behavior:     - Light rays enter the lens at different angles and emerge at different angles.     - Concave lenses cause incoming parallel light rays to spread out, a process known as diverging.     - The diverging rays appear to originate from a focal point located on the same side of the lens as the object itself.
• Image Formation:     - A concave lens always forms a virtual image.     - The image formed by a concave lens is always smaller than the actual object.
• Common Applications: Concave lenses are utilized in camera viewfinders and are often combined with mirrors or other lenses in optical instruments like telescopes.

Convex Lenses

• Physical Characteristics: A convex lens is curved outward at the center and is thinnest at its outer edges.
• Ray Behavior:     - As rays pass through, each is refracted to emerge at different angles.     - Convex lenses cause incoming parallel rays to come together, a process known as converging.     - Meeting Point: The converging rays meet at a focal point on the side of the lens opposite the object.
• Image Formation:     - Whether the produced image is real or virtual depends entirely on the distance of the object from the lens.     - Real Image: Formed when an object is located beyond the focal point.     - Virtual Image: A magnified virtual image is formed when the object is located between the focal point and the lens.
• Biological Example: A housefly’s eye consists of thousands of tiny individual eyes called facets. The outer surface of each facet is convex, which provides the fly with a nearly $360$-degree field of view.
• Common Applications:     - Slide projectors, movie projectors, and cameras.     - In movie theaters, film is placed upside down in the projector so the resulting real image on the screen appears upright.     - Historical Lighthouses: Used light sources placed at the focal point of a convex lens (or a series of them) to create a beam of parallel light rays.

Total Internal Reflection

• Total internal reflection is the complete reflection of a light ray back into its original medium.
• The Critical Angle: This is the specific angle of incidence that produces an angle of refraction of exactly $90$ degrees.     - At the critical angle, the light ray bends so significantly that it travels along the boundary between the glass and the air.     - At angles smaller than the critical angle, light is partly refracted and partly reflected.     - At angles larger than the critical angle, the light ray is reflected entirely back into the original medium (e.g., glass).
• Material Likelihood: Total internal reflection is most likely to occur in materials that possess small critical angles, as this causes most light entering them to be reflected internally.
• Fiber Optics Application:     - Fiber optics use total internal reflection to prevent light rays from exiting through the sides of curving fiber strands.     - This allows for the transmission of data in the form of light pulses over massive distances with minimal loss in signal strength.

Questions & Discussion

• Assessment Question 1: Light refracts when it passes from air to water because:     - a. the wavelength is different in the two media.     - b. the frequency is different in the two media.     - c. the speed is different in the two media.     - d. the amplitude is different in the two media.
• Assessment Question 2: The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a material.     - Answer: True
• Assessment Question 3 (Gemstones Table Interpretation): Which material is the most lustrous? The least lustrous?     - Answer: Moissanite is the most lustrous ($20.4\%$); emerald is the least lustrous ($4.8\%$).
• Assessment Question 4 (Gemstones Concepts): If a light ray strikes each material at an angle, in which material would the light ray bend the most?     - Answer: Light bends the most in moissanite because it has the greatest index of refraction.
• Assessment Question 5: Which type(s) of lens can form a real image?     - a. concave lens only     - b. convex lens only     - c. both concave and convex lenses     - d. neither concave nor convex lenses
• Assessment Question 6: What will happen to a ray of light if it hits a new medium at an angle greater than the critical angle?     - a. All the light will be refracted.     - b. Part of the light will be refracted and part reflected.     - c. All the light will be reflected.     - d. All the light will be absorbed.