THIN LENSES

THIN LENSES

Ø  Lenses are transparent materials that refract light. They are applied in the functioning of microscopes, the human eye, cameras, e.t.c.

Ø  There are two major types of lenses. (i)  the convex ( converging) lens

Ø  ( ii) concave ( diverging) lenses

Ø  Convex lenses can also be classified into three major types; the bi-convex, plano-convex and convex (converging) meniscus.

Ø  The concave lens may be classified into; the bi-concave, the plano-concave and the concave (diverging) meniscus.

o   DEFINITION OF TERMS

Ø  Centre of curvature (C) - this is the centre of the sphere of which the surface of lens is part of.

Ø  Radius of curvature (r) - this is the radius of the sphere of which the surface of the lens is part of.

Ø  Principal axis- the imaginary line passing through the centre of curvature.

Ø  Optical centre (O) - this is a point on the principal axis midway between the surfaces of the lens.

Ø  Principal focus (F)- the converging lens- the principal focus is a point on principal axis where rays parallel to the principal axis converge after refraction. For a diverging lens, the principal focus is the point on the principal axis where rays parallel to the principal axis appear to diverge from after refraction.

Ø  Focal length ( f)- is the distance between the optical centre and the principal focus.  For a converging lens it is real. For a diverging lens, it is virtual.

Ø  Focal plane- an imaginary line passing through the principal focus , along and perpendicular  to the principal axis  where rays that are not parallel to the principal axis converge or  appear to diverge

o   Ray DIAGRAMS

Ø  Three rays are normally used in drawing of diagrams.

Ø  (i) a ray of light parallel to the principal axis-  for a convex lens, the ray passes through the principal focus after refraction. For a concave lens, the ray appears to diverge from the principal focus after refraction.

Ø  (ii) a ray of light passing or appearing to pass through the principal axis-  the ray emerges parallel to the principal axis.

Ø  (iii) a ray of light through the optical centre- the ray passes on undeviated.

Ø  Ray diagrams are normally used to locate the image of a given object.

o   NB: it is important to note the following when drawing ray diagrams;

o   Real rays and real diagrams are drawn using full lines.

o   Virtual rays and virtual images are drawn by broken lines.

o   Where the rays intersect is the position of the image.

o   The symbols for the convex and concave lens that are normally used to locate images are shown below.

o   CHARACTERISTICS OF IMAGES FORMED ON THE LENSES

Linear magnification

It is defined as the ratio of the image to that of the object. It can also be defined as the ratio of the image distance to that of the object distance.

Therefore M= =    (using a typical diagram)

SCALE DRAWINGS

THE LENS FORMULA

DETERMINING THE FOCAL LENGTH OF A CONVERGING (CONVEX LENS)

RELATIONSHIP BETWEEN THE FOCAL LENGTH AND MAGNIFICATION

POWER OF A LENS

 The power of a lens is a property directly related to its focal length. It refers to the measure of its refracting ability.

 Power of a lens= 

The unit of power of a lens is dioptres (D).

The lens with a short focal length refracts light more and vice versa.

The convex (converging lens) have got positive power while the diverging (concave lens) have got negative power.

                                    APPLICATIONS OF LENSES

1.      SIMPLE MICROSCOPE/ MAGNIFYING GLASS-

2.      COMPOUND MICROSCOPE-

3.      THE HUMAN EYE-

Structure of the Eye

The amount of light entering the eye (right) is controlled by the pupil, which dilates and contracts accordingly. The cornea and lens, whose shape is adjusted by the ciliary body, focus the light on the retina, where receptors convert it into nerve signals that pass to the brain. A mesh of blood vessels, the choroid, supplies the retina with oxygen and sugar. Lacrimal glands (left) secrete tears that wash foreign bodies out of the eye and keep the cornea from drying out. Blinking compresses and releases the lacrimal sac, creating a suction that pulls excess moisture from the eye’s surface.

© Microsoft Corporation. All Rights Reserved.

Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.

The human eye acts as a natural optical instrument.

The main features of the eye include;

Sclerotic layer- is a hard shell enclosing the eye. It is white in color. The front part is the cornea.                 The cornea bends most of the light entering.

Aqueous humor- is a clear liquid between the lens and the cornea. It helps to maintain the shape                               of the eye.

Iris- this is the colored part of the eye. There is an opening called the pupil. The pupil allows                                 light to pass through. The iris changes the size of the pupil and therefore                                         controlling the amount of light passing through.

Crystalline lens- is a converging lens. The lens can change its focal length by the help of the                                      cilliary muscles (they either contract or relax).

Vitreous humor- a transparent jelly like substance filling the chamber between the lens and the                                 retina.

Retina- is made of light-sensitive cells. Images are normally formed here.

Fovea- this is the central part of the retina. The best details of the object images are formed here.

Blind spot- contains cells that are not light-sensitive.

Cilliary muscles- the lens is suspended by these muscles. They control the shape of the lens by                                  either contracting or relaxing.  When the muscles relax, the focal length                                    increases thus focus distant (away) objects and vice versa.

      The process through which the eye is able to change its focal length to focus both the near and distant objects is referred to as ACCOMODATION.

      Near point- this is the closest distance in which the normal eye can focus objects clearly. It is normally 25 cm.

      Far point- is the farthest point beyond which the normal eye may not focus clearly.

DEFECTS OF VISION

There are two common defects of vision

      The shortsightedness (myopia) - is caused by the eyeball being too long or short focal length.  The eye sees only near objects but not those that are far.

      The long sightedness (hypermetropia) - is caused by the eyeball being too short or the focal length being too long.  The eye focus clearly distant objects but not those that are near.

Focusing the Eye

Light rays entering the eye are refracted, or bent, when they pass through the lens. Normal vision requires that the rays focus on the retina. If the eyeball is too long, an accurately focused image falls short of the retina. This is called myopia, or nearsightedness. A nearsighted person sees distant objects unclearly. Farsighted focus, or hypermetropia, results when the eyeball is too short. In this case, an accurately focused image would fall behind the retina. These conditions can also occur if the muscles of the eye are unable to alter the shape of the lens to focus light rays accurately.

© Microsoft Corporation. All Rights Reserved.

Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.

CORRECTION OF SHORT AND LONGSITGHTEDNESS

-      Diverging lens is used to correct the short sightedness.

-      Converging lens is used to correct the long sightedness.

4.      THE CAMERA

      The camera is used for taking photographs

      The lens focuses light from the object to form an image on the film

      Focusing is done by either adjusting the distance between the lens and the film or moving away from or towards the object.

      The stop (or the diaphragm) - is an adjustable aperture that controls the amount of light entering the camera.

      The shutter allows light to pass through only for a precise period when the camera is being operated.

      The inside of the camera is blackened to absorb any stray light.

There are certain similarities between the eye and the camera

1.      The eye has a crystalline convex lens       the camera has a convex lens

2.      The choroid layer of the eye is black         the inside of the camera is painted black

3.      The eye has a retina where the images are formed     the camera has a light-sensitive                                                                                   film where images are formed

4.      The iris controls the amount of light entering the eye   the diaphragm (stop) controls                                                                      the amount of light entering the camera.

 Differences between the camera and the eye

1.      The focal lens of the eye is variable but for the camera is fixed.

2.      Only one image can be formed on the camera when the shutter of the camera is open while the eye forms constantly changing pictures.

3.      Cameras especially those with zoom lenses have variable image distances while the eye has a constant image distance.