Geometrical Optics – Part II Chapter 24 1

Going Backwards 2

Stuff  We continue with mirrors and lenses and even refractive surfaces.  Quiz on Friday  For a while, office hours will be in, of all places, my office. We really don’t need MAP-318 except before exams. And the hours are too confusing.  Next Exam is on Wednesday, December 2 nd.  I give up on the remaining evil clickers. Clicker grade=0.  Let’s move on. 3

4 When the Center of Curvature is on the same side of the R outgoing ray, R is positive. Otherwise, if the center of curvature is not on the same side R as the outgoing ray, R is negative.

Concave Mirror/Paraxial Approximation Consequently MIRROR EQUATION 5

Image Formation 6 ‘ ‘ y’<0 (from the diagram) so image is inverted.

The geometry…… 7

Let’s try an example 8

A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror cm 5 cm Normal to mirror and bounces back along incoming path.

A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror cm 5 cm

A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror cm 5 cm eye virtual image

The Concave Mirror 12

More Convex Mirror 13

Graphical Methods are very useful to check your work. 14

Moving on to refractive surfaces 15

Spherical Refractive Surfaces 16 air glass

A closer look at the Math …. 17

No for the height of the image 18

Check this out – how big is R? 19

From the math: 20

21

The Thin Lens  We ignore the thickness of the lens.  We will use mostly geometrical methods.  Any ray that bends is assumed to bend only once at the center of the lens. 22

From whence it came 23 Surface 1 Surface 2 n=1 n=1.5 n=1 Surface 2 n>1

The thin lens - geometry 24 parallel

More Geometry  Lens is thin  Actual thickness of the lens is ignored.  Image from first surface provides the object for the second surface.  Paraxial Ray Approximation  sin(x)=tan(x)=x  cos(x)=1  x is in RADIANS 25

More Geometry 26 Triangle PQO and triangle P’Q’O are similar. We will show that for a very thin lens: F 1 =F 2 =f The Thin Lens Equation

27 This, of course depends on where the object is placed with respect to f.

Thin Lens (con’t) 28 Image that would form if material “a” was all on this side of the lens. Object for second surface.

29 Procedure for equation Solve for image position for first surface Use image as object for the second surface. Use the refraction equation in both cases. For a lens. n a =n c =1 So we can call the middle one just n Mess with the algebra and you will get:

FINALLY – with some algebra and obvious substitutions, we get: 30 The Lensmaker’s Equation

Two Ways to do this STUFF  Algebraically using the lens equation (with the 1/f if you know it)  Using graphical Methods 31

Graphical Methods: 32

Graphical Methods: 33

Most important case: converging lens Object to left of F1 34

Most important case: converging lens 35

Most important case: converging lens 36

Most important case: converging lens 37

Most important case: converging lens 38

Most important case: converging lens 39