LIGHT

THIN LENSES

Name: ________________

Class: _________________

Index: ________________

At the end of this unit you should be able to :

1. Describe the action of converging lens and diverging lens on a beam of light.2. Define the term focal length of a converging lens.3. Draw a ray diagram to illustrate the formation of real and virtual images of an object by a converging lens.

Learning objectivesLearning objectives

Types of converging lens:A converging (or convex) lens is thicker in

the middle than at the edge.

(a) biconvex (b) plano-convex(c) concavo-convex

principalaxis

Optical centre, C

The principal axis of a lens is a line passing through the optical centre, C, of the lens and perpendicular to the plane of the lens.

Technical Terms:

principalaxis

Optical centre, C

The optical centre, C, of a lens is the point midway between the lens surfaces on its principal axis. Rays passing through the optical centre are not deviated.

F

F: focus

Focal length

C

The principal focus, F, of a thin converging lens is the point on the principal axis, to which an incident beam parallel to the principal axis is made to converge.

F

F

Focal length f

C F

The focal length, f, of a lens is the distance between the optical centre and the principal focus, F.

Focal Plane

The focal plane of lens is the vertical plane which passes through the principal focus and perpendicular to the principal axis.

F F

object

image

Object distance u

Image distance v

The object distance, u, is the distance between the optical centre and the object. The image distance, v, is the distance between the image and the optical centre. Since light can pass through a lens either the left or right side, a lens has two principal foci.

Construction of rays of a converging lens

Construction of rays of a converging lens

FC

F

Standard rays(For construction of ray diagram)

step 1 step2 step 3

The ray must parallel to the principal axle

Construction rules

Incident ray through the optical centre, CIncident ray parallel to the principal axisIncident ray directed towards principal focus,

F’

F’F C

object

Image

Formation of image by a converging lens:

Converging lens of focal length = fObject distance = uImage distance = v ( 6 Cases)

Given:

(continue on next slide)

2F F F

object

image

u

2f

v

u > 2f Nature of image: real, inverted and diminished

Uses: In a camera, in your eye at this moment

Case 1:

2F F F 2F

object

image

u

2f

v

u = 2f

Case 2:

Nature of image: real, inverted and same size

Uses: Photocopier

F F

object

image

u

f

v

f<u<2fNature of image: real, inverted and magnified

Uses: slide projector, film projector, objective lens of microscope

Case 3:

F F

object

u

f

u=f

No image is formed. (Image is formed at infinity). Depending on usage

Uses: spotlights, eyepiece of telescope

Case 4:

F F

object

image

u

f

v

0<u<fNature of image: virtual, upright and magnified

Uses: magnifying glass, spectacles for correcting long-sightedness

Case 5:

2F F F image

Object at infinite positionImage nature: real, inverted and diminished image

Uses: objective lens of telescope

v

f

Case 6:

F F

object

image

Worked example 1:Given: focal length of convex lens, f, object distance, u and its size. Find by graphically the size and the nature of its image produced.

The image obtained:Real, inverted andmagnified.Image distance, v > f

F F

image

object

Worked example 2:Given: focal length of convex lens, f, image distance, v and its size. Find graphically the size and the position of the object.

object

image

F

focal length f

Given: the size and position of distance of an object and its image . Find by graphically the focal length, f, and the position of the lens.

Worked example 3:

Formation of virtual images by a convex lens: (Case 5)

When an object is placed within the focal length of a convex lens, the image formed is virtual, upright and magnified.

This principal is used in a magnifying glass.

Virtual Image:

The image formed by this way is a virtual image, please explain?

To find the focal length of a convex lens:

Approximate method

Place a screen at the back of a convex lens. Adjust the position of the lens until a clear image of distance object is obtained on the screen. The distance between the lens and the screen gives the focal length of the convex lens.

Types of diverging lens:

A diverging (or concave) lens is thicker inat the edge than at the middle.

Action of diverging lens on a beam of light If the lens is concave, a beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens. The beam after passing through the lens appears to be emanating from a particular point on the axis in front of the lens; the distance from this point to the lens is also known as the focal length, although it is negative with respect to the focal length of a converging lens.

The Thin-Lens Equation and the Magnification Equation

Thin Lens Equation: 1/do + 1/di = 1/f

Magnification Equation: m = hi/ho = - di/do

Summary of sign conventions for lensesFocal length

f is + for a converging lens.

f is – for a diverging lens.

Object distance

do is + if the object is to the left of the lens (real object), as is usual.

do is - if the object is to the right of the lens (virtual object).

Image distance

di is + for an image (real) formed to the right of the lens by a real object.

di is - for an image (virtual) formed to the left of the lens by a real object

Magnification

m is + for an image that is upright with respect to the object.

m is - for an image that is inverted with respect to the object.

Example: A 1.70m tall person is standing 2.50m in front of a camera. The camera uses a converging lens whose focal length is 0.05m. (a) Find the image distance (the distance between the lens and the film) and determine whether the image is real or virtual. (b) Find the magnification and the height of the image on the film.

Solution:

(a) To find the image distance di, we use the thin-lens equation with do = 2.50m and f = 0.05m:

1/di = 1/f – 1/do = 1/0.05 – 1/2.50 = 19.6 m-1

di = 0.051m

Since the image distance is a positive number, a real image is formed on the film

(b) The magnification follows from the magnification equation:

m = - di/do = - (0.051/2.50) = -0.0204

The image is 0.0204 times as large as the object, and it is inverted since m is negative. Since the object height is ho = 1.70m, the image height is

hi = mho = (-0.0204)(1.70) = -0.0347m

Example: An object placed 7.10m to the left of a diverging lens whose focal length is f = -5.08cm (a diverging lens has a negative focal length). (a) Find the image distance and determine whether the image is real or virtual. (b) Obtain the magnification.

Solution:

(a) The thin-lens equation can be used to find the image distance di:

1/di = 1/f – 1/do = 1/(-5.08) – 1/7.10 = -0.338 cm-1

di = -2.96 cm

The image distance is negative, indicating that the image is virtual and located to the left of the lens.

(b) Since di and do are known, the magnification equation shows that

m = - di/do = - (-2.96/7.10) = 0.417

The image is upright (m is +) and smaller (m < 1) than the object.

Application of Converging Lenses

A camera consists of converging lens and light sensitive film mounted in a light-tight box. The lens can be moved to or fro so that a real, inverted, diminished and sharp image is focused on the film. The intensity of light that falls onto the film is controlled by a shutter and a variable aperture diaphragm. The shutter controls the length of time that the film is exposed to light. The diaphragm controls the aperture that allows light to pass through.

A projector essentially uses converging lenses to produce a real and magnified image. The condenser lenses direct the light through the slide or film to a projection lens. The projection lens is moved to and fro until a real, magnified and sharp image is focused to the screen. Since the image formed on the screen is inverted, the slide or film has to be put upside down. The real image formed on the screen is then the right way up.

A magnifying glass produces a virtual, upright and magnified image. The image appears to be larger and more distant than the object but it cannot be projected on a screen.

References

http://www.odec.ca/projects/2005/dong5a0/public_html/lenses.html

http://www.antonineeducation.co.uk/physics_a2/options/Module_6/Topic_2/ray_di

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http://www.mvlc.info/images/lighting_glossary_files/image007.gif

http://bloggingwoolf.files.wordpress.com/2008/12/magnifying-glass.jpg

http://www.colorado.edu/physics/phys1020/phys1020_sp05/labs/Lab4_Optics_files

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