Lecture 2: Reflection of Light: Mirrors (Ch 25) & Refraction of Light: Lenses (Ch 26)

Light - Electromagnetic Wave Wavefronts Rays Plane waves

Reflection of Light The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection equals the angle of incidence :

Formation of images by a plane mirror The image is upright. The image is the same size as you are. The image is located as far behind the mirror as you are in front of it.

Spherical Mirror CONCAVE Mirror Focal length of concave mirror = ½ R Spherical Aberration

Spherical Mirror Focal length of convex mirror = - ½ R CONVEX mirror Concave Solar Concentrators

Formation of image by CONCAVE mirror Ray 1, This ray is initially parallel to the principal axis and, therefore, passes through the focal point F after reflection from the mirror. Ray 2.This ray initially passes through the focal point F and is reflected parallel to the principal axis. Ray 2 is analogous to ray 1 except that the reflected, rather than the incident, ray is parallel to the principal axis. Ray 3.This ray travels along a line that passes through the center of curvature C and follows a radius of the spherical mirror; as a result, the ray strikes the mirror perpendicularly and reflects back on itself.

Formation of image by CONCAVE mirror

Formation of image by CONVEX mirror An object placed in front of a convex mirror always produces a virtual image behind the mirror. The virtual image is reduced in size and upright. Ray 1,This ray is initially parallel to the principal axis and, therefore, appears to originate from the focal point F after reflection from the mirror. Ray 2.This ray heads toward F, emerging parallel to the principal axis after reflection. Ray 2 is analogous to ray 1, except that the reflected, rather than the incident, ray is parallel to the principal axis. Ray 3.This ray travels toward the center of curvature C; as a result, the ray strikes the mirror perpendicularly and reflects back on itself.

The Mirror Equation and Magnification F = Focal length d o = Object distance d i = Image distance m = Magnification Concave mirror: The image distance is a positive quantity, as are the object distance and the focal length. If the Image is formed behind the mirror, the image distance is negative.

Summary of Sign Conventions for Spherical Mirrors Focal length f is + for a concave mirror. f is − for a convex mirror. Object distance do is + if the object is in front of the mirror (real object). do is − if the object is behind the mirror (virtual object). Image distance di is + if the image is in front of the mirror (real image). di is − if the image is behind the mirror (virtual image). Magnification m is + for an image that is upright with respect to the object. m is − for an image that is inverted with respect to the object.

Refraction and Snell’s Law Index of Refraction: n v = c/n, where c = speed of light in vacuum When light travels from a material with refractive index n1 into a material with refractive index n2, the refracted ray, the incident ray, and the normal to the interface between the materials all lie in the same plane. The angle of refraction is related to the angle of incidence by :

More on refraction and its effects Apparent depth: d’ = d (n 2 /n 1 )

Snell’s Law Derivation l

Total Internal Reflection Sparkle of Diamond Optical Fiber

Dispersion

Lenses

Formation of Image by Lenses

Thin Lens Equation and Magnification

Summary of Sign Conventions for Lenses Focal length f is + for a converging lens. f is − for a diverging lens. Object distance do is + if the object is to the left of the lens (real object), as is usual. do is − if the object is to the right of the lens (virtual object).** Image distance di is + for an image (real) formed to the right of the lens by a real object. di is − for an image (virtual) formed to the left of the lens by a real object. Magnification m is + for an image that is upright with respect to the object. m is − for an image that is inverted with respect to the object.

Lenses in Combination

The Human Eye Light travels through five different refractive index mediums before reaching the retina!

Near and Farsightedness Lasik: How does it work?

The Compound Microscope

The Telescope