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5.4 Lenses

Introduction

A lens is a transparent material which consists of at least one curved surface.

Images formed by lenses due to the phenomenon of refraction of light.

Rays of light travelling  through the optical centre pass through the lens in a straight line.

Rays of light from objects at infinity ( distant  objects) are parallel rays.

Types of lenses

 

(i) Convex lens @ Converging lens @ Positive lens

clip_image002

  (ii) Concave lens @ Diverging lens @ Negative lens

clip_image004

Common terminology of lenses

 

clip_image006

Optical centre , P            :            A point which all rays travelling through this point pass through the lens in a straight line.

 

Principal axis  , AB              :        A straight line which passes through  the optical centre ,P at a right angles to the plane of the lens.

 

Principal focus, F               :        A point on the principal  axis to which incident rays of

light travelling parallel to the principal axis , converge after refraction through a convex lens.

 

Or

 

A point on the principal  axis from which incident rays of light travelling parallel to the principal axis appear to diverge  after refraction through a concave lens.

 

 

Focal length , f                   :          The distance between the principal focus ,F and

                                                          the optical centre ,P.

               

Object distance , u               :        Distance of the object from the optical centre,P

 

Image distance , v                 :       Distance of the image  from the optical centre,P

 

Power of lenses  (P)

Power of a lens    =           1              .    

                                   Focal length

 

atau        P    =    1       @        P     =    100

                            f                                 f( cm)

 

The unit of power of a lens is Dioptre (D) or m-1

Convex lens  : the power is  taken to be positive

Concave lens  : the power is  taken to be negative

 

Example 1

 

A convex lens of focal length 40 cm. Determine the power of the lens.

Solution

 

Example 2

 

A lens with a power – 5D.

(a)           Calculate the focal length of the lens.

(b)           What is the type of the lens?

Solution

 

Experiment to estimate the focal length of a convex lens.

A convex lens is turned to face a distant object.

The position nof the screen is adjusted until a sharp inverted image is formed on the screen.

The distance of the screen from the optical centre of the lens is measured = x

The focal length of the lens = x

Experiment to estimate the power of a convex lens.

 

A convex lens is turned to face a distant object.

The position nof the screen is adjusted until a sharp inverted image is formed on the screen.

The distance of the screen from the optical centre of the lens is measured = x

The focal length of the lens = x

The power of the lens is determined by using the formula

 

 Power =         1          .

                Focal length

To determine the characteristics of images formed by convex and concave lens by using ray diagrams.

Ray diagrams for  Convex lens

 (a)   u < f

clip_image008

Solution:

clip_image010

(b)   u =  f

clip_image012

Solution:

clip_image014

(c)  f < u < 2f

clip_image016

Solution:

clip_image018

(d)  u = 2f

clip_image020

 Solution:

clip_image022

(e)  u > 2f

clip_image024

Solution:

clip_image026

(f)   u Þ ¥

     clip_image028

clip_image030

                                                          OR

      clip_image028

 

clip_image032

Conclusion:

Object distance ,u

Characteristics of image

  u < f

 

  u = f

 

   f <u< 2f

 

u = 2f

 

u > 2f

 

u = ∞

 

Ray diagrams for  Concave lens

 (a)   u < f

clip_image034

 

clip_image036

(b)    f < u < 2f

clip_image038

 

clip_image040

Conclusion:

Object distance ,u

Characteristics of image

  u < f

 

 f < u < 2f

 

To determine the characteristics of images formed by convex and concave lens by using lens equation.

 

Linear magnification, m

clip_image041

clip_image002

clip_image044

clip_image002[4]

                            OR

clip_image002[6]

 f = focal length

u = object distance

v = image distance

m = linear magnification

ho = object height

hi =  image height

Sign Conventions

 

 

Convex lens

Concave lens

Object distance ,u

Always +

Object is always placed to the left of the lens

Always +

Object is always placed to the left of the lens

Image distance, v

+  if the image  is real ( image is formed on the right side of the lens.

 

  if the image is virtual ( image is formed on the left side of the lens.

 

+  if the image  is real ( image is formed on the right side of the lens.

 

 

  if the image is virtual ( image is formed on the left side of the lens.

 

Focal length, f

Always +

 

Always –

 

Power of length, P

Always +

 

Always –

 

                                                                   

 

Linear magnification,m

Size  of image

I m I  = 1

Image  and object are the same size

I m I  > 1

Enlarged image

I m I  < 1

Diminished image

 

Example  3

An object of height  2 cm is placed at  30 cm  from a convex lens of focal length 20.0 cm. What is

(a)       the image distance

(b)       the linear magnification

(c)       the image height

(d)       the characteristics of the image

 

Solution

 

Example  4

An object of height  6 cm is placed at  20 cm  from a concave lens of  power  2.5 D.

What is

(a)     the image distance

(b)     the image height

(c)     the linear magnification

(d)     the characteristics of the image

 

Solution

 

Meaning of real image and virtual image 

A real image is one which can be cast on a screen.

A virtual image is one which cannot be cast on a screen.

 

Effect on the image produced when the upper portion of a lens is covered by a card.

 

The size and position of the image is the same as before. The brightness of the image, however , is reduced.

Experiment to investigate the relationship between the object distance,u and the image distance, v for a convex lens.

Hypothesis:

The image distance ,v  decreases as the object distance increases.

Aim of the experiment :

To investigate the relationship between the object distance,u and the image distance,v.

Variables in the experiment:

Manipulated variable: object distance,u

Responding variable: image distance, v

Fixed variable: focal length of the lens, f

List of apparatus and materials:

Convex lens, lens holder, white screen, cardboard with a cross-wire in a triangular cut-out , light bulbs and ruler

Arrangement of the apparatus:

clip_image050    

The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable.

The distance between the cardboard and the convex lens is measured by using a ruler , u

The screen is moved back and forth until a sharp image is formed on it.

The distance between the screen and the lens is measured , v.

The experiment is repeated 5 times for the other object distances ,u.

Tabulate the data:

u

 

 

 

 

 

 

v

 

 

 

 

 

 

Analysis the data:

 Plot the graph v against  u

clip_image052

 

Determination of the focal length by using graph method.

(i) Graph  clip_image054 against clip_image056 or  vice versa

                                            

 

            clip_image058

 

      From the equation ,       clip_image059

    Conclusion :

 

(ii) Graph u against  v or vice versa

 

                clip_image061

 

      From the equation ,        clip_image059       and        u = v

      

Conclusion :

(iii) Graph  m against  v

clip_image063

      From the equation ,clip_image059   and clip_image064

 

Conclusion :

 (iv) Graph  clip_image066 against  u

 

                clip_image068

      From the equation , clip_image059and      clip_image064 

      

Conclusion :

v) Graf v against m

clip_image069

 

Kecerunan graf adalah f

Pintasan paksi v adalah (0,f)

(vi) Graf u lawan clip_image066

                            

clip_image071

Kecerunan graf adalah f

Pintasan paksi u adalah (0,f)

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