Mirrors, Plane and Spherical Spherical Refracting Surfaces Geometric Optics Mirrors, Plane and Spherical Spherical Refracting Surfaces Thin Lenses Optical Instruments

General Definitions O is the object or its coordinate i is the image or its coordinate p is the distance of the object to a mirror, refracting surface or lens q (or i) is the distance of the image to a mirror , refracting surface or lens h is the object height h’ is the image height lateral magnification is the ratio of image height to object height an image is real if the light converges to form the image in space an image is virtual if the light appears to come from a place where it cannot

Methods of chararacterizing the light wave Wavefronts (3D surface of constant phase) Huygen’s Principle ray construction lines perpendicular to wavefronts showing direction of motion of wave the plane wave

Is this kind of plane mirror possible? Plane Mirrors Is this kind of plane mirror possible?

Plane Mirrors Illustrating formation of an image by a plane mirror. Since QR is common to both triangle PQR and triangle P’QR and q is is the same angle at vertex P and vertex P’ the right triangles are congruent, and p = - q, also h = h’ or the lateral magnification (M) is +1. The image is upright, the same size and left-right reversed.

Images from Mirrors

Why spherical surfaces? Easily made Good approximation to more complex surfaces such as parabolic Ubiquitous

Spherical Mirrors Definitions for the following terms Center of curvature (C) Radius of curvature (R or r) Principle Axis (or symmetry axis) Vertex (V)

Spherical Mirrors Concave mirrors: real and virtual images Note: Rays 1,2, and 3 are called principle rays. See your text.

Spherical Mirrors Note: Ray through C retraces itself

Mirror Eq

Spherical Mirrors

Spherical Mirrors Focus and focal length

Spherical Mirrors Sign Convention

Spherical Mirrors Convex mirrors: virtual images only Note: Rays 1,2, and 3 are called principle rays. See your text.

Spherical Refracting Surfaces

Spherical Refracting Surfaces Substituting for q’s using the last two equations yields Assume paraxial rays Exterior angle of a triangle is equal to the sum of opposite interior angles

Spherical Refracting Surfaces Flat refracting surfaces and apparent depth

Thin Lenses Two spherical refracting surfaces back to back Thickness of lens is small (negligible)

Thin Lenses For a thin lens in air, t is negligible At the left surface For a thin lens in air, t is negligible and n1 is equal to 1 At the right surface And

Thin Lenses We find that when we look at the focus of the lens

Thin Lenses Sign convention

Thin Lenses Converging and Diverging Lenses

Thin Lenses Converging and Diverging Lenses Principle Rays Note: Rays 1,2, and 3 are called principle rays. See your text.

Thin Lenses Converging and Diverging Lenses

Thin Lenses Multiple Lens Systems How do you locate the final image? Where is the final image?

Lens Aberrations Spherical & chromatic Astigmatism Coma

The Camera Aperture size determined by number expressing it as a ratio of focal length to opening called f-number

The Eye The camera is modeled after the eye “Normal” reading distance is 25 cm Eye is about 2.5 cm in diameter Most of focusing is done by the cornea and vitreous humor behind the cornea

Myopia Correct for the far point Power of lens Lens powers add

Hyperopia Correct for the near point

The SimpleMagnifier Measure angular magnifications For reading distance For infinite image

The Astronomical Telescope Object is at infinity so image is at f Measure angular magnification Length of telescope light path is sum of focal lengths of objective and eyepiece

The Compound Microscope Magnification is product of lateral magnification of objective and angular magnification of eyepiece Note: Image is viewed at infinity

Plane Mirrors Multiple plane mirror images and optical illusions

Two Plane Mirrors in One What concept from the previous chapter is important to this illustration? Where is this design used?

Spherical Aberration Aberration is reduced by considering rays close to the optic axis Rays are called paraxial rays (will be used for all spherical surfaces)