Reflection and Mirrors (Geometrical) Dr: HALA MOUSTAFA

Objectives: After completing this module, you should be able to: Explain and discuss with diagrams, reflection, absorption, and refraction of light rays. Illustrate graphically the reflection of light from plane, convex, and concave mirrors. Define and illustrate your understanding of real, virtual, erect, inverted, enlarged, and diminished as applied to images. Use geometrical optics to draw images of an object at various distances from converging and diverging mirrors.

Geometrical Optics In the study of how light behaves, it is useful to use “light rays” and the fact that light travels in straight lines. When light strikes the boundary between two media, three things may happen: reflection, refraction, or absorption. reflection refraction absorption Water Air

Reflection, Refraction, and Absorption Water Air reflection refraction absorption Water Air reflection Reflection: A ray from air strikes the water and returns to the air. refraction absorption Refraction: A ray bends into the water toward the normal line. Absorption: A ray is absorbed atomically by the water and does not reappear.

The Laws of Reflection 1. The angle of inci- dence qi is equal to the angle of reflection qr : Water Air N reflection qr qi qi = qr All ray angles are measured with respect to normal N. 3. The rays are completely reversible. 2. The incident ray, the reflected ray, and the normal N all lie in the same plane.

The Plane Mirror A mirror is a highly polished surface that forms images by uniformly reflected light. Note: images appear to be equi-distant behind mirror and are right-left reversed.

Definitions Object distance: The straight-line distance p from the surface of a mirror to the object. Image distance: The straight-line distance q from the surface of a mirror to the image. Object Image Object distance Image distance = p = q p q qi = qr

Real and Virtual Real images and objects are formed by actual rays of light. (Real images can be projected on a screen.) Real object Virtual image Light rays No light Virtual images and objects do not really exist, but only seem to be at a location. Virtual images are on the opposite side of the mirror from the incoming rays.

Image of a Point Object Plane mirror p q = p q Real object p q = p q Virtual image Image appears to be at same distance behind mirror regardless of viewing angle.

Image of an Extended Object Plane mirror p q q = p Virtual image Image of bottom and top of guitar shows forward-back, right-left reversals.

Terms for Spherical Mirrors A spherical mirror is formed by the inside (concave) or outside (convex) surfaces of a sphere. Concave Mirror R Axis V C A concave spherical mirror is shown here with parts identified. Linear aperture Center of Curvature C Radius of curvature R The axis and linear aperture are shown. Vertex V

The Focal Length f of a Mirror Since qi = qr, we find that F is mid- way between V and C; we find: Incident parallel ray qi R qr C V F axis f The focal length f is: Focal point The focal length, f The focal length f is equal to half the radius R

The Focus of a Concave Mirror The focal point F for a concave mirror is the point at which all parallel light rays converge. axis Incident parallel Rays C For objects lo- cated at infinity, the real image appears at the focal point since rays of light are almost parallel. F Focal point

The Focus of a Convex Mirror The focal point for a convex mirror is the point F from which all parallel light rays diverge. axis C F R Virtual focus; reflected rays diverge. Incident Rays Reflected Rays

Image Construction: Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror. C F Concave mirror Object C F Convex mirror Object Ray 1 Ray 1

Image Construction (Cont.): Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to the mirror axis. Concave mirror C F C F Convex mirror Ray 1 Ray 1 Ray 2 Ray 2 Image Image

Image Construction (Cont.): Ray 3: A ray that proceeds along a radius is always reflected back along its original path. Concave mirror C F C F Convex mirror Ray 2 Ray 1 Ray 3 C F Ray 2 Ray 1 Image Ray 3

The Nature of Images An object is placed in front of a concave mirror. It is useful to trace the images as the object moves ever closer to the vertex of the mirror. We will want to locate the image and answer three questions for the possible positions: 1. Is the image erect or inverted? 2. Is the image real or virtual? 3. Is it enlarged, diminished, or the same size?

Object Outside Center C 1. The image is inverted; i.e., opposite of the object orientation. Ray 1 Ray 3 Ray 2 C F 2. The image is real; i.e., formed by actual light rays in front of mirror. Concave mirror 3. The image is diminished in size; i.e., smaller than the object. Image is located between C and F

Object at the Center C 1. The image is inverted; i.e., opposite of the object orientation. Ray 1 Ray 2 C F 2. The image is real; i.e., formed by actual light rays in front of mirror. Ray 3 3. The image is the same size as the object. Image is located at C, inverted.

Object Between C and F 1. The image is inverted; i.e., opposite of the object orientation. Ray 1 Ray 3 C 2. The image is real; i.e., formed by actual light rays in front of mirror. F Ray 2 3. The image is enlarged in size; i.e., larger than the object. Image is outside of the center C

The parallel reflected rays never cross. Object at Focal Point When the object is located at the focal point of the mirror, the image is not formed (or it is located at infinity). Ray 1 Ray 3 C F Reflected rays are parallel The parallel reflected rays never cross. Image is located at infinity (not formed).

Object Inside Focal Point 1. The image is erect; i.e., same orientation as the object. C 2. The image is virtual; that is, it seems to be located behind mirror. F Virtual image Erect and enlarged 3. The image is enlarged; bigger than the object. Image is located behind the mirror

Observe the Images as Object Moves Closer to Mirror F Erect and enlarged Virtual image C F Ray 1 Ray 3 Ray 2 C F Ray 3 Reflected rays are parallel Ray 1

Image gets larger as object gets closer Convex Mirror Imaging C F Convex mirror C F Convex mirror Ray 1 Ray 1 Ray 2 2 Image Image gets larger as object gets closer All images are erect, virtual, and diminished. Images get larger as object approaches.

Converging and Diverging Mirrors Concave mirrors and converging parallel rays will be called converging mirrors from this point onward. Convex mirrors and diverging parallel rays will be called diverging mirrors from this point onward. C F Converging Mirror Concave C F Diverging Mirror Convex

Reflection and Mirrors (Geometrical)