Lenses (o-level)

LENSES

Are spherical surfaces of transparent materials. The materials maybe glass, plastics, water and so on.

 TYPES OF LENSES

They are two types namely:

(1) Converging lens   (convex lens)

(2) Diverging lens    (concave lens)

 

CONVERGING LENS

A convex lens is thick in the centre. It is also called converging lens because it bends light rays inwards.

Principal axis is the line through the optical centre “C” of the lens on which the principal focus lies.

Principal focus, F is the point on the principal axis at which all rays parallel and closed to the principal axis meet after refraction.

Optical Centre: The optical centre is the centre between poles of the lens at which the principal axis passes.

The pole of a lens is the centre point of the surface of the lens through which the principal axis passes.

TYPES OF CONVERGING LENSES

DIVERGENT LENS

A concave lens is thinnest in the central and spreads light out. A concave lens is also called a divergent lens because all rays that are parallel diverge after refraction.

Types of divergent

Note that:

(i) The principal focus of a converging lens is real while that of the diverging lens is virtual. The refracted ray seems to come from the point after refraction.

(ii) The real principal focus is one at which actual rays meet after refraction.

(iii) The focal .length is the distance between the principal focus and the optical centre.

 

RAY DIAGRAMS

An image can be formed by a lens when two of the following rays undergo refraction and meet at a point. The image will be formed by the meeting of refracted rays. The following are the rays which can be considered when drawing to obtain the image formed by a lens.

• A ray parallel to the principal axis is refracted through the principal focus. This ray can be selected from any point on the object.
• A ray through the optical centre (c) is undeviated, for a ray diagram, this ray is a line joining “C” to the point of the object where the parallel ray was selected.
• A ray through the principal focus is refracted parallel to the principal axis.

 

Ray diagram for various positions of the object in a converging lens

(a) Object at distance between f and 2f from lens.

The image is real inverted, magnified.

(b) Object at 2f

Image is: real, inverted, same size as the object

(c) Object at a distance greater than 2f from the lens

 

The image is: real, inverted diminished,

(d) Object at 2f

The image is real, inverted, same size as object

(e) Object at f.

(f) Object at distance less than f from the lens

         

The image is virtual, erect and magnified. A convex lens is used as a magnifying glass when the object is placed between the focal point and’ the lens because at this position the image formed is erect, magnified and virtual,

 

(f) Object at infinity

The image is: real, inverted and diminished.

A convex lens is used in microscopes magnifying glass, telescopes,

 

Ray diagram for position of object in concave lens

 The image formed in a diverging lens (concave lens) is always erect, virtual and diminished irrespective of the object distance from the lens,

 

Magnification of lens

 

The lens formula

If an object is a distance “u” from the lens and image distance v, then the focal length f is given by

This applies to both concave and convex lenses

 Sign convention

The convention is that;

(i)       distances of real images are positive

(ii)       distances of virtual images are negative

 

For a converging lens the focal length “f” is positive because it real  For a diverging lens the focal length f is negative because it virtual.

 

Example I: An object of height 10cm is placed at distance 50cn from a converging lens of focal length 20cm. Calculate (i) image position.

Example II

An object of height 10cm is placed at a distance of 60cm from a diverging lens of focal length 20crn. Find

 

(a) image position

Solution

h – 10cm, u – 60cm f = -20cm because the focal length for convex lens is virtual so it’s negative.

 

Finding the position by scale drawing

This will involve two steps:-

i) Select a scale for drawing

ii) Make a sketch of the drawing this should include two major rays from a point on the object. They are:

 

a) A ray which is parallel and closed to principle axis should refracted through focal point for converging lens while for diverging lens, the ray parallel is refracted in such a way that appears to come from the focal point

b) A ray through the optical centre should be drawn undeviated

iii)      Then a diagram is drawn to scale.

Example III:

An object of height 10 cm is placed a distance of 50cm from converging lens of focal length 20cm. Find by, scale drawing

i) Image position

ii) height of the image

iii) Nature of the image

h – 10cm                      u = 50cm                  f = 20cm

Example IV:

An object of height 10cm is placed at a distance of 60cm from diverging lens of focal length 20cm.

 

Find by scale drawing the

(i)  image position

ii) height of the image

iii)  nature of the image

iv) magnification

 

 

Experiment to measure the focal length of converging lens (convex lens) by

1. a) Illuminating object and plane mirror

Adjust the lens holder

The position of the lens holder is adjusted until a sharp image of the object is formed on the screen alongside the object itself. The object will now be situated at the focal point.

Measuring the focal length

The distance between the screen and the lens is measured and this is the focal length.

Note: At this position, the rays from the lens emerge as parallel rays and strike the mirror at right angle and they are reflected back along their original paths.

b) Measurement of object and Image

 

Setting the lens

The lens is set up in front of an illuminated object so that a real image is formed on the screen on the opposite side.

Adjusting the lens holder

The position of the lens holder is adjusted until a sharp image of the object is formed on the screen. Several pairs of distance of “u” and “v” are measured and the mean values for focal length f are obtained from

 

Example V:

Two converging lenses of focal lengths 15cm and 20cm are placed in contact. Find the power of the combination

Note:

The focal length of a converging lens is real so it is positive.

The focal length of diverging lens is virtual so it is negative.

 

Example VI:

A converging lens of focal length 20cm is placed in contact with diverging lens of focal   length diverging lens focal length  10cm. Find the  power  of combination focal length of converging lens f = 20cm

 

Application of lenses

Lens camera

• The lens focused light from the object on to film
• The diaphragm controls the amount of light reaching the film
• The shutter controls the exposure time of light reaching the film

 

 

 

Light enters the eye through the cornea (transparent), the lens and is focused on the retina.   The retina is sensitive to light and sends messages to the brain through the optic nerve.  The iris changes in size to vary the amount of light that enters through the pupil.   The size of the pupil decreases in bright light and increases in dim light.

 

Accommodation:   is the ability of the eyes the focus the images of objects at different distances on the retina.

Similarity between the human eye and camera

• The camera consists of a light-proof box which is black inside while the eye has a black pigment inside.
• Both the eye and camera have light sensitive pails. The retina for the eye and film for the camera
• Both the eye and camera have a lens,
• Both have a system which regulates the amount of light entering them, iris for the eye and diaphragm for the camera.

 

Differences between the human eye and the camera

Human eye	Camera
Lens: lens of human eye is biological	Lens: lens of the camera is artificial
Focal length: focal length of lens for the eye is variable	The Focal length: The focal length of lens the for camera is fixed
Distance: The distance between the lens and retina is fixed	Distance: The distance between the lens and film  is variable

                                                           

Defects of vision

Near point;   is the closest point at which one can see an object clearly. For an adult the near point is 25cm

Types of eye defects:

There are two types of eye defects namely: short sightedness and long sightedness.

a) Short sightedness

Here, a person who can see near objects clearly but cannot focus distant objects. This is because the eye ball is too long or the eye lens is too strong. The lens is too thick even though the ciliary muscles are relaxed.

Light rays from a distant object (infinity) are focused in front of the retina.

The defect is corrected by a concave spectacle lens which diverges the light before it enters the eye to give an image on the retina.

b)Long sightedness

A person can see distant objects clearly but cannot focus near objects. This is because the eye-ball is too short or eye lens is too thin even though the ciliary muscles are fully squeezed. This means that rays of light from the object are focused towards a point behind the retina.

The defect is corrected by a convex spectacle lens which converges the light to give an image on the retina.

 

PROJECTOR

A projector is used for projecting the image of a transparent slide onto the screen. So a projector forms a real image.

 Source of light:   The powerful source of light is placed at the principal focus of a concave mirror so as to illuminate the slide if the image is to be bright

Concave mirror:   The concave mirror reflects back light which would otherwise be wasted.

 Condenser: This is a combination, of two plane convex lenses. The main function is to collect the rays from the light source and concentrate them onto the slide

 The projector lens: The projector lens is mounted in a sliding tube so that it may be moved to and fro to focus a sharp image on the screen.

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