Geometric optics

Geometric Optics

Mirrors, light, and image formation

Geometric Optics

• Understanding images and image formation, ray model of light, laws of reflection and refraction, and some simple geometry and trigonometry• The study of how light rays form

images with optical instruments

REFLECTION AND REFRACTION AT A PLANE SURFACE

Reflection and refraction on plane mirrors

Key terms

• Anything from which light rays radiate–Object

• Anything from which light rays radiate that has no physical extent–Point object

• Real objects with length, width, and height–Extended objects

Key terms

Specular reflection

Reflection on a plane surface where reflected rays are in the same directions

Diffused reflection

Relfection on a rough surface

Key terms

Virtual image

Image formed if the outgoing rays

don’t actually pass through the

image point

Real image

Image formed if the outgoing rays actually pass through

the image point

Image formation by a Plane mirror


• a diagram that traces the path that light takes in order for a person to view a point on the image of an object

Ray Diagrams

• suggests that in order to view an image of an object in a mirror, a person must sight along a line at the image of the object.

Line of Sight Principle

SW1.9: Draw the rays and the image formed

Reflection at a Plane Surface


V

θ

θ

θ θ

s s’M M’


• M is the object and M’ is the virtual image

• Ray MV is incident normally to the plane mirror and it returns along its original path

• s= object distance• s’= image distance• s=-s’

Image formation by a Plane mirror• Sign rules

For the object distance:–When the object is on the same side of the

reflecting or the refracting surface as the incoming light, s is positive

For the image distance:–When the image is on the same side of the

reflecting or the refracting surface as the outgoing light, s’ is positive

Image of an extended object

V’

V

θθ

θ θ

s s’

y

M M’

Q Q’

θ

y’

Image of an extended object

• Lateral magnification–Ratio of image height to object height–M=y’/y

• Image is erect• m for a plane mirror is always +1• Reversed means front-back dimension

is reversed

REFLECTION AT A SPHERICAL SURFACE

Reflection on Concave and Convex mirrors

Reflection at a Concave Mirror

P P’CV


• Radius of curvatureR• Center of curvature• The center of the sphere of

which the surface is a partC

• Vertex• The point of the mirror surface

V

• Optic axisCV

IMAGE FORMATION ON SPHERICAL MIRRORS

Graphical Methods for Mirrors

Graphical Method

• Consists of finding the point of intersection of a few particular rays that diverge from a point of the object and are reflected by the mirror

• Neglecting aberrations, all rays from this object point that strike the mirror will intersect at the same point

Graphical Method

• For this construction, we always choose an object point that is not on the optic axis• Consists of four rays we can usually

easily draw, called the principal rays

Graphical MethodA ray parallel to the axis, after reflection passes through F of a concave mirror or appears to come from the (virtual) F

of a convex mirror

A ray through (or proceeding toward)

F is reflected parallel to the axis

A ray along the radius through or away from C intersects the surface

normally and is reflected back along its original path

A ray to V is reflected forming equal angles

with the optic axis

Object is at F

Object is between F and Vertex

Object is at C

Object is between C and F

Positions of objects for concave mirrors


FCV

s at infinity s’= R/2


• All reflected rays converge on the image point• Converging mirror• If R is infinite, the mirror

becomes plane


The incident parallel rays converge after reflecting from the

mirror

They converge at a F at a distance R/2

from V

F is Focal point, where the rays are brought to focus

f is the focal length, distance from the vertex to the focal

point

f= R/2


FCV

s’ at infinity s= R/2


The object is at the

focal points=f=R/2

1/s +1/s’= 2/R 1/s’=0; s’ at infinity

1/s+ 1/s’= 1/fObject image relation, spherical mirror

Image of an Extended Object

m= y’/yLateral

magnification

m= y’/y= -s’/sLateral

magnification for spherical mirrors

Reflection at a Convex Mirror

F C

s or s’ at infinitys’ or s= R/2

Image formation on spherical mirrors

• Sign rulesFor the object distance:–When the object is on the same side

of the reflecting or the refracting surface as the incoming light, s is positive; otherwise, it is negative


• Sign rulesFor the image distance:–When the image is on the same side

of the reflecting or the refracting surface as the outgoing light, s’ is positive; otherwise, it is negative


• Sign rules:For the radius of curvature of a spherical

surface:–When the center of curvature C is on

the same side as the outgoing light, the radius of curvature is positive, otherwise negative


• The convex side of the spherical mirror faces the incident light

• C is at the opposite side of the outgoing rays, so R is neg.

• All reflected rays diverge from the same point

• Diverging mirror


Incoming rays are parallel to the optic

axis and are not reflected through F

Incoming rays diverge, as though they had come from point F behind the mirror

F is a virtual focal point

s is positive, s’ is negative

Example • Santa checks himself for soot, using his

reflection in a shiny silvered Christmas tree ornament 0.750m away. The diameter of the ornament is 7.20cm. Standard reference work state that he is a “right jolly old elf,” so we estimate his height to be 1.6m. Where and how tall is the image of Santa formed by the ornament? Is it erect or inverted?

• s’= -1.76cm; m= 2.34x10-2 ; y’= 3.8cm

REFRACTION AT A SPHERICAL SURFACE

Refraction at spherical interface

Refraction at a Spherical Surface

VC

GRAPHICAL METHOD FOR LENSES

Biconcave and biconvex thin lenses

Lenses

Lenses

Biconvex lens; converging

Biconcave lens; diverging

LensesOnly F is needed for the

ray diagram

Chief ray through

the center is

undeviated

Ray parallel is refracted in such a

way that it goes through F on transmission

through the lens

Focal ray is parallel to the axis of transmission

For concave lens, the rays appear to have passed through F on

the object’s side of the lens

Lenses

An object is placed 30cm from a biconcave lens with a focal length of 10cm. Determine the image characteristics graphically.

Geometric optics

Education

Transcript of Geometric optics