Spherical Mirrors

Ray Diagrams - Concave

• Ray 1 – from the top of the object parallel to the principal axis and reflected through the focal point F

• Ray 2 – from the top of the object through the focal point and reflected parallel to the principal axis

• Ray 3 – from the top of the object through the center of curvature C and reflected back on itself

Ray Diagrams - Concave

Ray Diagrams - Concave

Ray Diagrams - Concave

Ray Diagrams - Convex

Ray Diagrams - Convex

• Ray 1 – from the top of the object parallel to the principal axis and reflected away from the focal point F

• Ray 2 – from the top of the object toward the focal point on the back side of the mirror and reflected parallel to the principal axis

• Ray 3 – from the top of the object toward the center of curvature C on the back side of the mirror and reflected back on itself

Ray Diagrams - Convex

Sample Problem

• A convex mirror has a radius of curvature of 25.0 cm. Find graphically the image of an object in the form of an arrow perpendicular to the axis of the mirror at each of the following object distances:

• A.) 30.0 cm• B.) 20.0 cm• C.) 10.0 cm, and• D.) 5.0 cm

Quiz # 3

A concave mirror has a radius of curvature of 60.0 cm. Calculate the image position and magnification of an object placed 90.0 cm from the mirror. Describe the resulting image. Draw the ray diagram of the system and show that this coincides with your computed value. Note: scale is 1:10

Thin Lenses

Image Formation by Refraction

Thin Lenses

Thin Lenses

Thin Lenses

• A converging lens is of focal length 10.0 cm. Locate the image of objects placed

• A.) 30.0 cm,• B.) 10.0 cm and• C.) 5.0 cm from the lens

Ray Diagrams - Lenses

The Human Eye

The Human Eye

• Accommodation – focusing on an object by varying the shape of the crystal lens

• Near point – closest distance for which the lens can accommodate to focus the light on the retina

• Far point – the greatest distance for which the lens of the relaxed eye can focus light on the retina.

The Human Eye

Farsightedness - hyperopia

Nearsightedness - myopia

Total Internal Reflection• Occurs when light

passes from a medium of higher refractive index into one of smaller refractive index.

• All the incident light is reflected back into the medium

• Critical angle – when the angle of refraction is 90O.

Total Internal Reflection

• Using Snell’s Law,

2 21 2

1 1

sin90sin ,( )cn n n n

n n

Total Internal Reflection

• A beam of light is propagating through diamond (n1 = 2.42) and strikes a diamond-air interface at an angle of incidence of 28O. (a) Will part of the beam enter the air (n2 = 1.00) or will the beam be totally reflected at the interface? (b) If the diamond is surrounded by water (n2 = 1.33) instead?

Total Internal Reflection

• Applications in fiber optics

Dispersion

• Spreading of light into its color components• Index of refraction of many materials (i.e.

glass) depends on the wavelength

• Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh?