Applied Physics for the School of Engineering Technologies PHY143 Braum Barber

Optics: Light, Mirrors & Lenses PHY143 Braum Barber

Electromagnetic Spectrum White light is made up of a band of electromagnetic waves with different frequencies. Visible light ranges from 400 to 700 nm

Electromagnetic Spectrum Outside the visible range includes radio waves, microwaves, infrared, ultraviolet, x- rays, and gamma rays.

Speed of Light The speed of light is constant. c = 3.00 x 10 8 m/s c = f x λ where f = frequency [s -1 or Hz] λ = wavelength [m]

Law of Reflection The angle of incidence equals the angle of reflection.

Reflection of Light The direction of the propagation of light can be changed as it is reflected off of a surface.

Spherical Mirrors

The outside of a spherical mirror is a convex mirror, the inside is concave. The center of the sphere is the center of curvature.

Focal Point The focal point for a spherical mirror is half of the mirror radius.

Images using a Spherical Mirror: Ray Tracing (Graphical Method) From the top of an object draw a parallel ray that reflects through the focal point. Draw a focal ray through the focal point, and a line parallel at the intersection with the mirror. Draw a center-of-curvature ray through the center of the sphere. The intersection will show the height and location of the image.

Images using a Convex Mirror

Object SizeOrientationType of Image AnywhereSmaller UprightVirtual

Images using a Concave Mirror

Object SizeOrientationType of Image Beyond C SmallerInverted Real At CSameInvertedReal Between C & F LargerInvertedReal Just beyond F Nearing infinite InvertedReal Just inside F Nearing infinite UprightVirtual Between F & surface LargerUprightVirtual

The Mirror Equation 1/d 0 + 1/d i = 1/ƒ

Magnification m = h i /h o = -d i /d o

Sign Rules Focal Length: Positive for concave mirrors Negative for convex mirrors Magnification:Positive for upright images Negative for inverted images di:Positive for real images Negative for virtual images

Problem Using a mirror with a focal point of 25 cm, we would like to create a virtual image that is twice the size of the original object. The original object is 12 cm high, 15 cm wide, and 7.0 cm deep.

Refraction of Light The speed of light will decrease as it passes through denser materials. v = c/n Where c = 3.00 x 10 8 m/s ( speed in a vacuum ) n is the index of refraction v is the velocity of light through different substances.

Snell’s Law n 1 sinΘ 1 = n 2 sinΘ 2

Index of Refraction Glass 1.45 Ice1.31 Ethyl Alcohol1.36 Water1.33 Air 1.00

Refraction When a ray of light enters a medium where its speed decreases, it is bent towards the normal. When a ray of light enters a medium where its speed increases, it is bent away from the normal.

Critical Angle At a certain angle, the light will totally reflect off of the surface (and no light refracts). sin Θc = n 1 /n 2

Critical Angle

Problem You are standing on the edge of a pool and you see your watch lying on the bottom about 2 m from the edge of the pool. The pool indicates that the depth of the water is 3 m where you are looking. Your eyes are approximately 1.8 m from the pool deck. Where is the watch actually located?

Lenses Light can be focused or dispersed using lenses.

Convex Lenses Convex lenses can be used to focus light.

Images using a Convex Lens: Ray Tracing (Graphical Method) The parallel ray intercepts the midpoint of the glass and the focal point. The focal-point ray pass through the lens to the focal point and a parallel line is draw. The midpoint ray passes through the midpoint of the lens. The intersection of these lines indicates the size of the image.

Image using a Convex Lens

Convex Lenses Always produce REAL and INVERTED images.

Image on a Concave Lens

Concave Lenses Always produce VIRTUAL, UPRIGHT, & SMALLER images.

Thin Lens & Magnification Equations 1/d 0 + 1/d i = 1/ƒ m = h i /h o = -d i /d o

Sign Rules Focal Length: Positive for convex lenses Negative for concave lenses Magnification:Positive for upright images Negative for inverted images di:Positive for real images Negative for virtual images

Problem There is an object that is 3.00 m high, 2.50 m wide and 1.25 m long. It is located 12 m in front of a convex lens with a focal length of 3.25 m. Describe the image produced.

Transit

Level

Aberrations Spherical Aberration: –Causes the light to focus at different focal points. Chromatic Aberration –Caused by the different wavelengths of light refracting at different angles

Summary An understanding of how light behaves in reflection and refraction allows the learner to predict the performance of different optical devices. Aberrations will reduce the performance of your optical device, though some of these may be corrected.