Physics 23: Light--Geometric Optics

1. Physics 23: Light--Geometric Optics Christopher Chui Physics 23: Light--Geometric Optics - Christopher Chui

2. The Ray Model of Light • Light travels in straight lines • Geometric optics refers straight-line rays of light at various angles • Reflection: When a narrow beam of light strikes a flat surface, the angle of incidence, qi, is the angle an incident ray makes with the normal to the surface. The angle of reflection, qr, is the angle the reflected ray makes with the normal • For flat surfaces, the incident and reflected rays lie in the same plane with the normal: qi = qr Physics 23: Light--Geometric Optics - Christopher Chui

3. Formation of a Virtual Image by a Mirror • The image appears as far behind the mirror as the object is in front: the image distance, di, equals the object distance, do. The height of the image is the same as that of the object. • It is a virtual image, because the image would not appear on a paper or film placed at the location of the image. Physics 23: Light--Geometric Optics - Christopher Chui

4. Formation of Images by Spherical Mirror • A spherical mirror is called convex if the reflection takes place on the outer surface of the spherical shape. A mirror is called concave if the reflection surface is on the inner surface of the sphere • The point F, where rays parallel to the principal axis come to a focus, is called the focal point of the mirror. The distance between F and the center of the mirror, length FA, is the focal length, f. • Focal length of mirror, f = r/2. Physics 23: Light--Geometric Optics - Christopher Chui

5. Finding the Image Position for a Curved Mirror • Ray 1 is drawn // to the axis; therefore, it must pass along a line through F after reflection • Ray 2 is drawn through F; therefore it must reflect so it is // to the axis • Ray 3 is chosen to be perpendicular to the mirror, and is drawn so that it passes through C, the center of curvature. Because it is perpendicular, it will be reflected back on itself • Object distance, do, is the distance of the object to the center of the mirror • Image distance, di, is the distance of the image to the center of the mirror Physics 23: Light--Geometric Optics - Christopher Chui

6. Mirror Equation • 1/do + 1/di = 1/f where f is the focal length • f= r/2 where r is the radius of curvature of mirror • Lateral magnification, m, is height of image / height of object: m = hi / ho = - di / do • Hi is +ve if the image is upright, -ve if inverted • Di and do are +ve if both image and object are on the reflecting side of the mirror, otherwise –ve • Magnification is +ve for an upright image and –ve for an inverted image Physics 23: Light--Geometric Optics - Christopher Chui

7. Convex Mirror • The image of a convex mirror is always virtual and erect • The radius of curvature of a convex mirror is negative by conventionfocal length is -ve Physics 23: Light--Geometric Optics - Christopher Chui

8. Problem Solving for Spherical Mirrors • Always draw a ray diagram, which serves as a check • Use the mirror equation and follow the sign convention • When the object, image, or focal point is on the reflecting side of the mirror (on the left side), the corresponding distance is considered +ve. If any of these points is behind the mirror (on the right), the corresponding distance is –ve. • The image height hi is +ve if the image is upright, and –ve if inverted, relative to the object (ho is always +ve). Physics 23: Light--Geometric Optics - Christopher Chui

9. Index of Refraction • The ratio of the speed of light in vacuum to the speed v in a given material is called the index of refraction, n, where n = c / v • Refraction: Snell’s law: n1 sin q1 = n2 sin q2 • Total internal reflection—light passes from a material into a 2nd material with smaller index of refraction, the light bends away from the normal—at a particular incident angle, the angle of refraction will be 90o. This incident angle is called the critical angle, qc • sin qc = (n2 / n1) sin 90o = n2 / n1 Physics 23: Light--Geometric Optics - Christopher Chui

10. Thin Lenses; Ray Tracing • Any lens that is thicker in the center than at the edges will make // rays converge to a point, and is called a converging lens • Lens that are thinner in the center than at the edges are called diverging lenses because they make // rays diverge • The power P of a lens = 1/f • The unit for lens power is the diopter, D • 1 D = 1 m-1 Physics 23: Light--Geometric Optics - Christopher Chui

11. Find the Image Position of a Thin Lens • Ray 1 is drawn // to the axis; it is refracted by the lens so it passes along a line through the focal point F • Ray 2 is drawn on a line passing through the other focal point F’ and emerges from the lens // to axis • Ray 3 is directed toward the center of the lens; this ray emerges from the lens at the same angle as it entered. The image is REAL and inverted; hi and m are negative • For diverging lens, the image is VIRTUAL and upright. di and f are negative; hi and m are positive • Lens equation: 1/do + 1/di = 1/f • Lateral magnification, m = hi / ho = - di / do • Power of a converging lens is +ve; a diverging lens is -ve Physics 23: Light--Geometric Optics - Christopher Chui

12. Problem Solving for Lenses • Read and reread the problem • Draw a ray diagram. Draw two or three rays • Solve for unknowns in the lens equation and the magnification. Don’t forget reciprocals • Follow the sign conventions • Check your analytic solutions are consistent with your ray diagram Physics 23: Light--Geometric Optics - Christopher Chui