Optics The Study of Light

Areas of Optics Geometric Optics Light as a ray. Physical Optics Light as a wave. Quantum Optics Light as a particle.

Optical images Nature Orientation Size real (converging rays) virtual (diverging rays) Orientation upright inverted Size true enlarged reduced

Law of Reflection Angle of incidence equals angle of reflection. r i

Plane Mirror + - Image -5 cm object 5 cm

Spherical mirrors shiny shiny concave convex + - + - (where reflected rays go) (dark side) (where reflected rays go) (dark side) concave convex Focal length, f, is positive Focal length, f, is negative

Parts of a Spherical Concave Mirror + - Vertex Center Focus Principle axis

Spherical Concave Mirror (object outside center) F Real, Inverted, Reduced Image f

Spherical Concave Mirror (object at center) F Real, Inverted, True Image

Spherical Concave Mirror (object between center and focus) Real, Inverted, EnlargedImage

Spherical Concave Mirror (object at focus) No image

Spherical Concave Mirror (object inside focus) Virtual, Upright, Enlarged Image

Parts of a Spherical Convex Mirror + - Principle axis Focus Center

Spherical Convex Mirror F C Virtual, Upright, Reduced Image

Mirror equation #1 1/si + 1/so = 1/f si: image distance so: object distance f: focal length

Mirror equation # 2 M = -si/so = hi/ho si: image distance so: object distance hi: image height ho: object height M: magnification

Concave vs convex mirrors Image is real when object is outside focus Image is virtual when object is inside focus Focal length f is positive Convex Image is always virtual Focal length f is negative

Real vs Virtual images Real Virtual Formed by converging light rays si is positive when calculated with mirror equation Virtual Formed by diverging light rays si is negative when calculated with mirror equation

Upright vs Inverted images Always virtual if formed by one mirror or lens hi is positive when calculated with mirror/lens equation Inverted Always real if formed by one mirror or lens hi is negative when calculated with mirror/lens equation

Definition: Refraction Change in speed of light as it moves from one medium to another. Can cause bending of the light at the interface between media.

n = c/v n = Index of Refraction speed of light in vacuum speed of light in medium n = c/v n =

Snell’s Law n1sin 1 = n2sin 2 n1 n2 1 2 angle of incidence angle of refraction

n1 < n2 light bends toward normal 1 n1 n2 2

n1 > n2 light bends away from normal 1 n1 2 n2

Dispersion The separation of white light into colors due to different refractive indices for different wavelengths.

Dispersion Due to different indices of refraction for different wavelengths of light.

Critical Angle of Incidence Light would refract 90o so it reflects instead, undergoing total internal reflection. r n2 n1 > n2

Calculating Critical Angle n1sin(1) = n2sin(2) n1sin(90o) = n2sin(2) n1 = n2sin(c)

Total Internal Reflection Occurs only when angle of incidence > critical angle n2

Announcements 4/16/2017 Turn in homework (lens problems) on overhead. Lab report will be due next week (on looseleaf or graph paper).

Consider a lens with f = 20 cm. You place a 5 cm tall object 30 cm in front of the lens. Draw the ray diagram and construct the image. Calculate the image distance and height using the lens/mirror equations. Name the image.

Converging lens #1 + - 2F F C F 2F Real, Inverted, Reduced Image

Converging lens #2 + - 2F F C F 2F Real, Inverted, True Image

Converging lens #3 + - 2F F C F Real, Inverted, Enlarged Image

Converging lens #4 + - F C F Virtual, Upright, Enlarged Image

For converging lenses f is positive so is positive si is positive for real images and negative for virtual images M is negative for real images and positive for virtual images hi is negative for real images and positive for virtual images

Diverging lens + - F C F Virtual, Upright, Reduced Image

For diverging lenses f is negative so is positive si is negative M is positive and < 1 hi is positive and < ho