Chapter 33 Lenses and Optical Instruments

32-5 Refraction: Snell’s Law Example 32-8: Refraction through flat glass. Light traveling in air strikes a flat piece of uniformly thick glass at an incident angle of 60, as shown. If the index of refraction of the glass is 1.50, (a) what is the angle of refraction θ A in the glass; (b) what is the angle θ B at which the ray emerges from the glass?

32-6 Visible Spectrum and Dispersion The visible spectrum contains the full range of wavelengths of light that are visible to the human eye.

32-6 Visible Spectrum and Dispersion This spreading of light into the full spectrum is called dispersion. If Light goes from air to a certain medium:

If light passes into a medium with a smaller index of refraction, the angle of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90°; this is called the critical angle: 32-7 Total Internal Reflection;

If the angle of incidence is larger than the critical angle, no refraction occurs. This is called total internal reflection Total Internal Reflection; Fiber Optics

Conceptual Example 32-11: View up from under water. Describe what a person would see who looked up at the world from beneath the perfectly smooth surface of a lake or swimming pool.

Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (a) or diverging (b) Thin Lenses; Ray Tracing

Thin Lenses Converging Diverging Thickest in the center Thickest on the edges

Parallel rays are brought to a focus by a converging lens (one that is thicker in the center than it is at the edge) Thin Lenses; Ray Tracing

A diverging lens (thicker at the edge than in the center) makes parallel light diverge; the focal point is that point where the diverging rays would converge if projected back Thin Lenses; Ray Tracing

The power of a lens is the inverse of its focal length: Lens power is measured in diopters, D: 1 D = 1 m Thin Lenses; Ray Tracing

Ray tracing for thin lenses is similar to that for mirrors. We have three key rays: 1.The ray that comes in parallel to the axis and exits through the focal point. 2.The ray that comes in through the focal point and exits parallel to the axis. 3.The ray that goes through the center of the lens and is undeflected Thin Lenses; Ray Tracing

Thin Lenses: Converging Principle axis 1.Parallel ray goes through f 2.Ray through center 3.Ray through f comes out parallel f object image Image: Upright or upside down Real or virtual Bigger or smaller f Focal point is on both sides of the lens equidistant from the lens

Thin Lenses: Diverging 1.Parallel ray goes through f 2.Ray through center is straight 3.Ray through f comes out parallel fobjectimage Upright or upside down Real or virtual Bigger or smaller Image: f For lenses virtual images are formed in front of the lens f

The sign conventions are slightly different: 1.The focal length is positive for converging lenses and negative for diverging. 2.The object distance is positive when the object is on the same side as the light entering the lens (not an issue except in compound systems); otherwise it is negative. 3.The image distance is positive if the image is on the opposite side from the light entering the lens; otherwise it is negative. 4.The height of the image is positive if the image is upright and negative otherwise The Thin Lens Equation; Magnification

33-2 Magnification: Magnification = image height / object height = - image distance (q) / object distance (p) p -q q p Negative m = upside down Negative q =virtual

Lens Equation Sign Conventions for lenses and mirrors Quantity Positive “ + ”Negative “ - ” Object distance p Real*Virtual* Image distance, qReal and behind the lens Virtual and same side as object Focal length, f ConvergingDiverging Magnification, m UprightUpside down f≠p+qf≠p+q

Image Applet ens/lens_e.html

33-2 The Thin Lens Equation; Magnification Example 33-2: Image formed by converging lens. What are (a) the position, and (b) the size, of the image of a 7.6-cm-high leaf placed 1.00 m from a mm-focal-length camera lens?

33-2 The Thin Lens Equation; Magnification Example 33-3: Object close to converging lens. An object is placed 10 cm from a 15-cm- focal-length converging lens. Determine the image position and size (a) analytically, and (b) using a ray diagram.

In lens combinations, the image formed by the first lens becomes the object for the second lens (this is where object distances may be negative). The total magnification is the product of the magnification of each lens Combinations of Lenses

Example 33-5: A two-lens system. Two converging lenses, A and B, with focal lengths f A = 20.0 cm and f B = 25.0 cm, are placed 80.0 cm apart. An object is placed 60.0 cm in front of the first lens. Determine (a) the position, and (b) the magnification, of the final image formed by the combination of the two lenses.