GEOMETRIC OPTICS

To understand images and image formation, all we need are the RAY MODEL OF LIGHT, the LAWS OF REFLECTION and REFRACTION, and some simple geometry and trigonometry.

GEOMETRIC OPTICS

• The study of how light rays form images

REFLECTION AND REFRACTION AT A PLANE SURFACE

OBJECT

• Anything from which light rays radiate• Could be:– Light emitted by the object itself (self-

luminous)– Light emitted by another source and then

reflected from the object

• POINT OBJECT has no physical extent.

• EXTENDED OBJECT has length, width and height.

• Point P an object point

• Point P’ an image point

“The reflecting surface forms an image of point P.”

TYPES OF IMAGES

• Virtual image if the outgoing rays don’t actually pass through the image point

• Real image the outgoing rays do pass through an image point.

Image formation by a Plane Mirror

SIGN RULES

Lateral Magnification

• The ratio of image height to object height

• If the image is erect, m is positive• If the image is inverted, m is negative

REFLECTION AT A SPHERICAL SURFACE

Concave and Convex Mirrors

CONCAVE MIRRORS

• Center of Curvature (C)• Radius of Curvature (R)• Vertex, the center of

the mirror surface (V)• Optic axis, the line CV

Focal Point and Focal Length

• Where:f = focal lengthR = radius of curvature

• Where:s = object distances’= image distancef = focal length

Lateral Magnification (m)

SAMPLE PROBLEM

• A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and the image size.

SAMPLE PROBLEM

CONVEX MIRRORS

• The center of curvature (C) is on the opposite side to the outgoing rays

Sample Problem

CONCAVE AND CONVEX MIRROR

CONCAVE MIRROR

• has the capability of forming images that can be smaller or larger in size and virtual or erect, depending on the position of the object.

CONVEX MIRROR

• always produces a smaller, virtual, and erect image of an object.

• In convex mirror, the length of the image is shorter than that of the object.

CONCAVE MIRROR

• doctors use this mirror for obtaining a relatively larger image of teeth, ear, skin etc.

CONVEX MIRROR

SW : REFLECTION ON SPHERICAL SURFACE

½ c.w. DO NOT COPY THE PROBLEM. SHOW COMPLETE SOLUTION

1. A luminous object is 4.00 m from a wall. You are to use a concave mirror to project an image of the object on the wall, with the image 2.25 times the size of the object. How far should the mirror be from the wall? What should the radius of curvature be?

1. Determine the image distance and image height for a 5.00-cm tall object placed 20.0 cm from a concave mirror having a focal length of 15.0 cm.

2. Find the focal length of a convex mirror of an object 0.30 m from the mirror forms an image of 0.10 m behind the mirror.

GRAPHICAL METHOD FOR MIRRORS

Concave Mirror

• The center C of a concave mirror is outside the mirror.

• Focal point F is also outside the mirror, half way between the center and the surface of the mirror.

• The focal length f is half of the radius.

case 1: case 1: The object is placed at a distance The object is placed at a distance greater than the C. The image formed is greater than the C. The image formed is

real, inverted and smaller in size.real, inverted and smaller in size.Step 1 Step 2

Step 3 Step 4

case 2: The object is placed at a distance equal to C. The image formed is real,

inverted and the same size as the object.

Case 3: The object is placed between C and f. The image formed is real, inverted

and magnified in size.

Case 4: The object is located at f. No image is formed.

Case 5: The object is placed between the principal focus and the mirror. The

image formed is virtual, upright and magnified.

CONVEX MIRRORS

PRINCIPAL RAYS:

PRINCIPAL RAYS:

PRINCIPAL RAYS:

PRINCIPAL RAYS:

PRINCIPAL RAYS:

THIN LENSES

THIN LENS

• A lens is an optical system with two refracting surfaces

• The simplest lens has two spherical surfaces close enough together that we can neglect the distance between them (the thickness of the lens)

CONVERGING LENS• Has the property that when a beam of rays

parallel to the axis passes through the lens, the rays converge to a point F2 and form a real image at that point.

• Similarly, rays passing through point F1 emerge from the lens as a beam of parallel rays.

• A positive lens (F1 and F2 are both positive)

DIVERGING LENS

• The beam of parallel rays incident on this lens diverges after refraction.• Is called a negative lens• The focal length of a diverging lens is

a negative quantity

GRAPHICAL METHOD FOR LENSES

GRAPHICAL METHOD FOR LENSES

GRAPHICAL METHOD FOR LENSES

Sample Problem

• An object 5.0 cm high is placed 24 cm away from a lens of focal length 8.0 cm.

a.Calculate the location of the imageb.Calculate the height of the image

SHORT QUIZ

OPEN NOTES (1/2 CW) DO NOT COPY THE PROBLEM…SHOW GIVEN AND COMPLETE SOLUTION

1. An object 5.0 cm high is placed 24.0 cm away