Geometric Optics

Reflection, Refraction and

Lenses 

Refraction in LensesOBJECTIVES

Understand how light is refracted and transmitted through lenses to form images.

Know the difference between concave and convex lenses?

Master the skill of constructing ray diagrams of objects in front of lenses to predict where an image will be and what it will look like.

Lenses

• Convex• Concav

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Lens is a piece of transparent material, such as glass or plastic, that is used to focus light and form an image.

Convex Lenses• Convex lens is thicker at the center than at the edges

• Convergent lenses because they refractparallel light rays so that the rays meet at a point – focal point.

• Rays from distant objects are parallel So focal point can be found by locating point where the suns rays are brought to a sharp image

F

• Lenses are thinner in the middle than around the edges.

• Divergent lenses because when surrounded by material with a lower index of refraction, rays passing through it spread out.

• The focal point is the point from which the diverging rays seem to emerge

Concave Lenses

F

Convex Lens

Principalaxis

C Fxx

Ax

fR

C: Center of curvatureR: Radius of curvature (2f)F: Focal Pointf: focal lengthA: vertex, center of lens

Optical axis

Fx

R

xC

f

Lens

C Fxx

Ax

The image location of an object in front of a lens is the location where all its light intersects after refracting and passing through the lens. The image is the intersection point of all refracted rays.

Fx x

C

Object

Ray tracingTo find the image of an object, we will trace a few rays through the lens and see where they intersect. The intersection of rays after passing through the lens locates the image of the object

Ray tracing is a method of constructing an image using the model of light as a ray.

We use ray tracing to construct optical images produced by mirrors and lenses

Ray tracing lets us describe what happens to the light as it interacts with a medium

C

Fxx

Ax

Fx x

C

Object

Ray Diagram-Convex lens

Principal ray

Focal ray

Central ray

Image of top

of object

Image

This Image isLocated opposite

side, beyond C

Real Inverted and Enlarged in size

Ray tracingTo find the image of an object, use the following principal rays

• the p-ray, which travels parallel to the principal axis, then refracts through the focal point.

• The f-ray, which travels through the focal point, then refracts parallel to the principal axis.

• The c-ray, which travels through the center of the lens and continues without bending.

Ray Diagram-Concave lens

Object f f

Principal ray

Focal ray

Central ray

Image

This Image isLocated same side,

inside fVirtual (on same

side) Upright and Reduced in size

Optical Image Location Orientation

• upright• inverted

Size• True• Enlarged• Reduced

Type• real (converging rays)• virtual (diverging rays)

OBJECT Location CONVEX Lens IMAGE

Location Orientation Size Type

Beyond C Between C and FOther side inverted Reduced real

At C At C Other Side Inverted True real

Between C and F

Beyond COther side Inverted Enlarged real

At F NO IMAGEInside F Same Side Upright Enlarged Virtual

OBJECT Location CONCAVE Lens IMAGE

Location Orientation

Size Type

Very far away Inside FSame Side Upright Reduced Virtual

Very close Inside FSame Side Upright Reduced Virtual

The Lens Equationdo di

Object ff Image

hi

ho

f

fd

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h

h

Thin Lens EquationThe thin lens equation relates the focal length of a spherical thin lens to the object position and the image position

di is positive for real images

di is negative for virtual images

f is positive for convex, converging lensesf is negative for concave, diverging lenses

Lateral Magnification

o

i

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d

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hi is positive for upright images

hi is negative for inverted images

Example: Image formed by converging lens. What is a) the position and b) the size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal length camera lens?

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a) Image is behind lens, only 2.6 mm farther from the lens than would be the image for an object at infinity.

Example: Image formed by converging lens. What is a) the position and b) the size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal length camera lens?

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b)

Image is 4 mm high and inverted (m<0)

Example: Object close to a converging lens. An object is placed 10 cm from a 15 cm focal length converging lens. Determine the image position and size (a) analytically and (b) using a ray diagram

f f

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since di<0, image is virtual and on same side of the lens.Since m>0, image is upright

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Example: Object close to a converging lens. An object is placed 10 cm from a 15 cm focal length converging lens. Determine the image position and size (a) analytically and (b) using a ray diagram

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b)

Image is virtual and upright

Example: Diverging lens. Where must a small insect be placed if a 25 cm diverging lens is to form a virtual image 20 cm in front of the lens?

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DO NOW

An object is located 139.0 mm from a 50 mm focal length converging lens. Find the image distance and magnification a) by using a ray diagram b) by calculation

f f

a)

Image is real, inverted and reduced

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units

units

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DO NOW

An object is located 139.0 mm from a 50 mm focal length converging lens. Find the image distance and magnification a) by using a ray diagram b) by calculation

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http://www.phys.ufl.edu/~phy3054/light/lens/applets/Welcome.html

http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/index.html

Lenses

DO NOWAn object 31.5 cm in front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this and what is its focal length? Is the image real or virtual? Confirm with ray diagram.

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a)

Lens is divergingcmf

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Chromatic Aberration • Light that passes through a lens is ringed with

color – This results from dispersion of light by the lens– Always present when a single lens is used– Can be corrected by using two lenses

Our Eyes & LensesLight that is emitted or

reflected off an object travels into the eye through the cornea.

The light then passes through the lens and focuses onto the retina that is at the back of the eye.

Specialized cells on the retina absorb this light and send information about the image along the optic nerve to the brain.

Focusing Images

Light entering the eye is mostly focused by the cornea because the air-cornea surface has the greatest difference in indices of refraction (cornea n=1.376).

The lens is responsible for the fine focus that allows you to clearly see both distant and nearby objects.

Accommodation • Muscles surrounding the lens can

contract or relax, thereby changing the shape of the lens.

This, in turn, changes the focal length of the eye. When the muscles are relaxed, the image of distant objects is focused on the retina.

When the muscles contract, the focal length is shortened, and this allows images of closer objects to be focused on the retina.

Distant vision

Close vision

Nearsightedness

– Focal length of the eye is too short to focus light on the retina.

– Also known as myopia

– Objects far away are blurry

– Fixed with concave lenses

Farsightedness–Focal length of the

eye is too long and places image past the retina

–Also known as hyperopia

–Objects nearby are blurry

–Fixed with convex lenses

Camera

Example: An 80 mm focal length lens is used to focus an image on the film/sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 120mm.A) how far ahead of the film should the lens be if the object to be photographed is 3.0 m away??B) What is the closest object this lens could photograph?

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a)

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Example: An 80 mm focal length lens is used to focus an image on the film/sensor of a camera. Maximum distance allowed between the lens and the sensor plane is 120mm.B) What is the closest object this lens could photograph?

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Refracting Telescope– Lenses magnify distant objects– Light from stars and galaxies so far

away that light is parallel and makes a real image

Objective lens Eyepiece

Binoculars– Lenses produce magnified images of faraway

objects• Just as separation of your eyes gives a sense of 3D

and depth, the prisms allow greater separations of the objectives, thereby improving 3-D

Microscope– Used to view very small objects