Wave Optics Lesson 3 New concepts ✓ Diffraction ✓ Reflection ✓ Refraction ✓ Virtual image ✓ Real image Diffraction • Diffraction is the bending of a wave around the edges of an opening or an obstacle. Reflection • Reflection is a phenomenon that occurs when a wave or object bounces off an interface or another object. • Law of reflection: The angle of incidence = the angle of reflection Reflection • For reflection of light off a flat mirror or other shiny, flat surfaces, the image formed is called a virtual image. • A virtual Image • an image formed by light rays that appear to originate from a point. • A real image • an image formed by light rays that do originate from a point. Reflection plane mirror • The image formed in a plan mirror: ➢ Virtual image. ➢ Equal the object in size. ➢ Reversed. ➢ At equal distance from the mirror as the object. ➢ Upright. Waves at an Interface • The speed of a wave depends on properties of the medium. • At an interface where properties of the medium change, • wave speed and wavelength also change, with a resulting change in direction . Slowing Down Speeding Up Refraction v. experiment • Refraction is the change in direction of a wave as a result of the change in wave speed at different points along the wave front. • Refraction happens for all types of waves. • The refraction of light waves can also result in the formation of images Wave Front Model Huygens’ Wave Model Snell’s law: The relation between velocities and directions of light passing from one medium to another. Snell’s law: • The index of refraction of a material: is the ratio of the speed of light in a vacuum to the speed of light in that material. Snell’s law: 50) A ray of light moving through air strikes the surface of an unknown transparent liquid at an angle of 40.0° with respect to the normal. The ray is observed to refract at an angle of 26.1. Determine the index of refraction for and the speed of light in the unknown liquid. Given 𝜃1 = 40° 𝜃2 = 26.1° 𝑛1 = 1 𝑛2 = ? The law 𝒏𝟏 𝒔𝒊𝒏𝜽𝟏 = 𝒏𝟐 𝒔𝒊𝒏𝜽𝟐 𝟏 × 𝒔𝒊𝒏 𝟒𝟎 = 𝒏𝟐 𝒔𝒊𝒏(𝟐𝟔. 𝟏) 𝒏𝟐 = 𝟏 ×𝒔𝒊𝒏 𝟒𝟎 𝒔𝒊𝒏(𝟐𝟔.𝟏) = 𝟏. 𝟒𝟔 Snell’s law: A ray of light moving through air strikes the surface of an unknown transparent liquid at an angle of 45.0° with respect to the normal. The ray is observed to refract at an angle of 30.0°. The index of refraction for air is 1.00, and the speed of light in a vacuum is 𝟑 × 𝟏𝟎𝟖 m/s. Determine the index of refraction for and the speed of light in the unknown liquid. Given 𝜃1 = 45° 𝜃2 = 30° 𝑛1 = 1 𝒏𝟐 = ? 𝒗 =? 1 2 𝒏𝟏 𝒔𝒊𝒏𝜽𝟏 = 𝒏𝟐 𝒔𝒊𝒏𝜽𝟐 𝟏 × 𝒔𝒊𝒏 𝟒𝟓 = 𝒏𝟐 𝒔𝒊𝒏(𝟑𝟎) 𝒏𝟐 = 𝟏 ×𝒔𝒊𝒏 𝟒𝟓 𝒔𝒊𝒏(𝟑𝟎) = 𝟏. 𝟒 𝒔𝒊𝒏𝜽𝟏 𝒔𝒊𝒏𝜽𝟐 = 𝒗𝟏 𝒗𝟐 𝒔𝒊𝒏(𝟒𝟓) 𝒔𝒊𝒏(𝟑𝟎) = 𝟑 × 𝟏𝟎𝟖 𝒗𝟐 𝒗𝟐 × 𝒔𝒊𝒏 𝟒𝟓 = 𝟑 × 𝟏𝟎𝟖 × 𝒔𝒊𝒏(𝟑𝟎) 𝟑 × 𝟏𝟎𝟖 × 𝒔𝒊𝒏(𝟑𝟎) 𝒗𝟐 = = 𝟐. 𝟏𝟐 × 𝟏𝟎𝟖 𝒔𝒊𝒏 𝟒𝟓 Lenses • A lens: a piece of glass or other transparent substance with curved sides that is used for concentrating or dispersing light rays. • Lenses bend light by refraction. • A converging lens (convex lens): a lens shaped so that all rays entering parallel to the optical axis converge at a single point on the opposite side of the lens. • A diverging lens (concave lens): a lens shaped so that all parallel rays appear to diverge away from a single point on the same side of the lens. Lenses • The focal point: (F) The point at which the rays converge or appear to diverge. • The focal length: ( f ) The distance from the focal point to the lens. • Which is determined by the index of refraction and the shape of the lens. • The curvature of the lens determine the focal length. • Flatter lens has longer focal length. • The optical axis: An imaginary line that goes through the center of the lens and is perpendicular to the lens plane. Formation of Images Ray tracing is used to determine where and what type of images will form when a light ray travels from an object through a lens. Real images form on the opposite side of the lens, compared to the object’s position. Virtual images form on the same side of the lens as the object. geometric-optics Magnification Magnification the process of making an object appear larger. Magnification The Lens Equation: It is a mathematical model you can use to calculate image locations. The Lens Equation: Problem: A rubber duck is placed 0.33 m from a converging lens that has a 0.28 m focal length. Use the lens equation to calculate the image distance and the magnification. Indicate whether the image is real or virtual and upright or inverted. The image distance is ………… m. The magnification is ……………….. . Is the image real or virtual? …………………….. Is the image inverted or upright? ……………………………..
