Optics Cheat Sheet b2qw

High School Physics - Core Concept Cheat Sheet

17: Geometric Optics Key Physics

Geometric Optics Problem Solving Tips

• Plane mirror: A flat reflective surface. Creates an image that is virtual, upright, the same size and that appears to be as far behind the mirror as original is in front. • Law of reflection: The angle of incidence equals the angle of reflection. Angles are measured relative to a line normal to the surface. • Normal line: A line drawn perpendicular to the surface. • Virtual image: The rays of light do not actually through the image; they just seem to originate from that location. Cannot be projected onto a screen. • Diffuse reflection: Reflection from a rough surface where variations in the direction of the surface cause light to reflect in different directions. • Concave mirror: A curved surface that focuses parallel rays of light to a single point, the focal point. Image type, size, and orientation depend on objects position. Also called a converging mirror. • Convex mirror: A curved surface that diverges light as if it originates from a point behind the mirror, the focal point. Forms a virtual image. Also called a diverging mirror. • Focal length: Distance from the lens or mirror to the focal point. • Center of curvature: Twice the focal length of a lens or mirror. This represents the center of the spherical surface if it was extended. • Real image: An image where the rays of light actually through the image. It can be projected onto a screen. • Ray diagram: A tool for tracing the path of light incident on a lens or mirror, assumes light is a straight line. • Refraction: The bending of light due to a change in its velocity in various media. • Index of refraction: The ratio between the speed of light in a vacuum and speed of light in a particular medium. • Dispersion: The separation of light into colors by refraction. Used in prism and cause of rainbows. • Total internal reflection: The complete reflection of light when it strikes the boundary between two media at greater than a critical angle. Used in fiber optics. • Convex lens: A converging lens that gathers incoming parallel light rays to a single focal point. Image may be real or virtual depending on objects position. • Concave lens: A diverging lens that diverges light as if it originates from a point in front of the lens, the focal point. Forms a virtual image, smaller, upright image. • Spherical aberration: A lens defect where light is imperfectly focused near the focal point. • Chromatic aberration: A lens defect where various color focus at different locations.

Variables Used and Key Metric Units • • • • • • • • •

f= focal length of mirror or lens. Units, m do=objects distance from the mirror or lens. Units, m di= images distance from the mirror or lens. Units, m n= index of refraction hi= height of image. Units, m ho= height of object. Units, m m = magnification v= velocity of light in a particular medium. Units, m/s θ= angle between given ray and normal line. Units, degrees

These tips will make it easier to solve any physics problems. • Thoroughly read the entire problem. • Draw a ray diagram carefully. • Identify all given information. • Identify the quantity to be found. • Select appropriate formula(s) that incorporate what you know and what you want to find. Pay extra attention of sign conventions. • Convert units if needed. • Do any mathematical calculations carefully.

Ray Diagrams object

2f

Focal point

Focal point

Image

With this convex lens notice how the rays travel and meet when the image is formed. In this case, a real, magnified, inverted image is formed.

Rays meet to give an inverted, real, larger image.

image Focal point

In this case, a virtual, smaller, and upright image is formed.

Mirror/Lens Type

Object Position Beyond C At C Between F & C At F In front of F

Concave Mirror Or Convex Lens Convex Mirror Or Concave Lens

Anywhere

With this convex mirror, notice how the rays don’t actually meet. You must trace the rays backwards into the mirror to see where they seem to originate.

Type of Image Real Real Real None Virtual Virtual

Orientation/ Size Inverted, smaller Inverted, same Inverted, larger None Upright, larger Upright, smaller

Sign Conventions • • • • •

Virtual images are –di Real images are +di Converging optics have +f Diverging optics have –f Objects distance is always +do

Example Refraction Diagram Θair Air, n=1.00 Glass, n=1.52 Θglass

Key Formulas and Constants

Note how the beam bends to the normal when entering the more dense glass medium. Then it bends away from the normal when re entering air.

Air, n=1.00 • 1/f=1/do+1/di Θair • m=hi/ho=-di/do • n=c/v • n1sinθ1=n2sinθ2 • speed of light in a vacuum, c = 3.0 x 108m/s • refractive index of air = 1.00 How to Use This Cheat Sheet: These are the keys related this topic. Try to read through it carefully twice then rewrite it on a blank sheet of paper. Review it again before the exams.

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