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# Types of lenses, image formation in lenses, lens formula and calculations

LENSES

Lenses are used as magnifying glasses.  They are also used in microscopes, telescopes, cameras and projectors.  The human eye has a natural lens and which enables people to see clearly.  There are two types of lenses: Converging and Diverging lenses.

The converging lens brings light rays together while the diverging lens spreads light rays apart.

A converging (convex) lens bulges at the centre while diverging lens gets thinner at the centre.

TERMINOLOGIES

Terms which are commonly used in lenses include, principal axis of a lens, the principal focus of a lens, optical centre of a lens, and focal length of a lens.  The principal axis of a lens is the line joining the centre of curvature of the two surfaces of the lens, and passing through the middle of the lens.

The principal axis of a lens is the line joining the centre of curvature of the two surfaces of the lens, and passing through the middle of the lens.

The principal focus of a lens is the point on the principal axis to which all rays parallel and close to the axis converge or diverge, after refraction the lens.  The principal focus of a converging lens is real, while that of a diverging lens is virtual.  The optical centre of lens is defined as the centre of the lens which is a point on the principal axis of the lens.  Rays of light which pass through the optical centre are undeviated.  The focal length of a lens is the distance between the optical centre and the principal focus of the lens.

FORMATION OF IMAGES IN LENSES

COVERGING LENS

To produce the image of an object by a converging lens, two major rays are required:

(1)     A ray from the top of the object incident on the middle, c, of the lens and passes through the lens undeviated.

(2)     A ray from the top of the object parallel to the principal axis, incident on the lens, and refracted through the principal focus, F.  At the point where these two rays interact, the image of the object is formed.

OBJECT AT INFINITY

When an object is very far from the lens i.e at infinity, the image is real, inverted and formed at the focus of the object beyond 2f1.

OBJECT BEYOND 2F1

When an object is very far from the les i.e at infinity, the image is real, inverted and formed at the focus of the object beyond 2f1.

OBJECT BEYOND 2F1

When an object is placed beyond 2F1, the image of the object is formed between F and 2F and is real, inverted and smaller than the object (diminished).

POWER OF A LENS

The power of a lens is the reciprocal of the focal length of a lens in metres.

P = 1/f

THE SIMPLE MICROSCOPE OR MAGNIFYING GLASS

A complex lens gives an enlarged upright virtual image of an object placed inside the principal focus.  This constitutes a simple microscope.  It is used for reading and studying biological specimens.

CLASSWORK 2

1. (a) Define the focal length of a converging lens
• Draw a simple ray diagram of an object placed at the center of curvature of a converging lens and when between the center of curvature and the focus
1. A small image is viewed through a converging lens held close to the eye. If the focal length of the lens is 10cm and a virtual image of height 2cm is formed 30cm away from the lens, obtain by calculation (i) the distance of object from the lens (ii) the size of the object

ASSIGNMENT 2

SECTION A

1. The image formed by a converging lens is 3 times as tall as the object. If the focal length of the lens is 12cm, calculate the distance of the image from the object (a) 16cm (b) 48cm (c) 32cm (d) 64cm
2. Which of the following correctly describe the image formed by a diverging lens? (a) Diminished, erect and virtual (b) Diminished, inverted and real (c) Magnified, erect and virtual (d) Magnified, inverted and real
3. The distance between optical centre and twice the principal focus of a lens is called……. (a) Optical centre (b) focal length (c) principal axis (d) radius of curvature
4. A pin 6cm high is placed in frontof a diverging lens of focal length 15cm. calculate the position of the image formed (a) -15cm (b) 15cm (c) -10cm (d) 10cm
5. Calculate the power of a converging lens with a focal length of 5cm (a) +0.0D (b) +0.2D(c) -20.0 (d) -0.2D
6. An object is placed 20cm from a converging lens. If the real image formed is 80cm. Find the focal length of the lens? (a)15cm (b) 30cm (c) 10cm (d) 16cm
7. Inability of the eye to focus near objects is known as: (a) astigmatism (b) hypermetropia (c) myopia (d) presbyopia
8. An object placed 15cm from a converging lens from a real image whose magnification is 2.0. What is the focal length of the lens? (a) 10.0cm (b) 6.00cm (c) 5.00cm (d) 1.50cm
9. A converging lens produces an image four times as large as an object placed 25cm from the lens. Calculate its focal length (a) 100cm (b) 33cm (c) 29cm (d) 20cm
10. A convex lens of focal length 15cm forms a real image 45cm from the lens. Find the magnification of the image (a) 1 (b) 2 (c) 3 (d) 4

SECTION B

1. (a) Define the following terms (i) focal length (ii) principal axis of a converging lens

(b) Distinguish between a real and a virtual image and draw ray diagrams to illustrate how a converging lens can be used to produce each type of image

1. The screen of a pinhole camera is a square of side 0.16m and it is 0.15m behind the pin hole. The camera is placed 11m from a flag staff and positioned so that the image of the flag staff is formed centrally on the screen. The image occupies three quarters of the height of the screen. What is the height of the flag staff?
2. Draw the ray diagram of an object placed (i) at F (ii) at 2F (iii) between 2F and F of a converging lens