# Image formation by Lenses

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Image formation by Lenses
Chitranjan Kumar Lecturer, G.P.C.G., Jalandhar

In daily life, you may have come across two types of lenses that are
1. thicker or 2. thinner in the middle. Which of the following items do you think may contain lenses? Eye glasses. Peep-hole. Camera. Magnifying glasses. Security mirror.

What happens to the light when it
When you see through lenses, do the objects appear the same as they are? No ! What happens to the light when it passes through a lens

Introduction Lenses are very useful.
e.g. in cameras, projectors, telescopes, microscopes and eyes The most common lenses: spherical lenses (i.e. the surface is spherical)

1 Convex and concave lenses
Convex lens - thicker at the centre than at the edge. Bi-convex Plano-convex Convex-concave

1 Convex and concave lenses
Concave lens - thinner at the centre than at the edge. Bi-concave Plano-concave Convex-concave

1 Convex and concave lenses
Converging or Diverging? convex lens concave lens (converging lens) (diverging lens)

1 Convex and concave lenses
Converging or Diverging? convex lens concave lens (converging lens) (diverging lens)

1 Convex and concave lenses
Converging lens bend the light inwards You may remember ‘converging’ as ‘concentrating’.

1 Convex and concave lenses
Diverging lens bend the light outwards You may remember ‘diverging’ as ‘dividing’.

1 Convex and concave lenses
Converging or diverging? Recall that light travels more slowly in glass than in air. Light converges or diverges as some parts of the wavefronts lag behind. converges diverges

Key features of lenses

Parallel rays are refracted inwards.
Convex Lens Parallel rays are refracted inwards. Refracted rays meet at a point called principal focus F

Centre of the lens is called the optical centre C.

The distance of F from C is the focal length f of the lens.

A convex lens has 2 principal foci.
1 on each side F F' F F' C principal axis The line through the optical centre and 2 foci is called the principal axis.

Parallel rays are refracted outwards.
Concave Lens Parallel rays are refracted outwards. Refracted rays appear to spread from a point called principal focus

Centre of the lens is called the optical centre C.

The distance of F from C is the focal length f of the lens.

A concave lens has 2 principal foci. 1 on each side
principal axis The line through the optical centre and 2 foci is called the principal axis.

Q1 A light ray is incident on a convex lens.
Which one represents the path of the light ray? X Y Z A Path X. B Path Y. C Path Z.

Q2 A light ray is incident on a concave lens.
Which one represents the path of the light ray? X Y Z A Path X. B Path Y. C Path Z.

2 Image formation by a lens
When the light from a point of an object enters our eyes, we can see the point. screen O I

2 Image formation by a lens
a Real images Light rays converge to a point. O I

2 Image formation by a lens
Image can be captured by a screen. Hence called ‘real’. screen O I

2 Image formation by a lens
b Virtual images Light rays diverge from a point. I O No rays actually come from the image. concave lens Hence called ‘virtual’.

2 Image formation by a lens
b Virtual images Light rays diverge from a point. I O convex lens

Since only convex lenses converge light rays, real images can only be formed by convex lenses.
screen O I

3 Graphical construction of image formation
a Construction rules In ray diagrams, we use symbols to represent lenses. convex lenses concave lenses

…is refracted through F.
Construction rules for convex lenses Rule 1 A ray parallel to the principal axis... F C …is refracted through F.

…is refracted parallel to the principal axis.
Rule 2 A ray passing through F'... F' F C …is refracted parallel to the principal axis.

Rule 3 A ray passing through C... F' F C …travels straight on.

The 3-ray diagram again Ray 1: Parallel to axis, then passes through far focal point Ray 2: Passes unchanged through center of lens Ray 3: Passes through near focal point, then parallel to axis

Real image, inverted, smaller
F f Object ho do Real image, inverted, smaller hi di

Construction rules for concave lenses
A ray parallel to the principal axis... C F' F …is refracted so that it appears to come from F'.

…is refracted parallel to the principal axis.
Rule 2 A ray directed towards F... C F' F …is refracted parallel to the principal axis.

Rule 3 A ray directed towards C... C F' F …travels straight on.

The 3-ray diagram again Ray 1 Parallel to axis, virtual ray passes through near focal point Ray 2 Straight through center of lens Ray 3 Virtual ray through far focal point, virtual ray parallel to axis

Virtual image, upright, smaller
Object ho do Virtual image, upright, smaller hi di F f F

Images formed by a convex lens
Object : At infinity F I 2F C 2F' F' Image: at F , real, inverted and diminished

Object : Beyond 2F ’ 2F O F I C 2F' F' Image: Between F and 2F , real, inverted and diminished

Object : At 2F ’ 2F F O I C 2F' F' Image: At 2F , real, inverted and same size

Object : Between F ’ and 2F ’ O F 2F I C 2F' F' Image: Beyond 2F ,real, inverted and magnified

Object : At F ’ F 2F O C 2F' F' Image: At infinity

Object : < F ’ I 2F F O C 2F' F' Image: On the same side as the object virtual, erect and magnified

Images formed by a concave lens
Object : At infinity 2F F I C 2F' F' Image: At F’

virtual, erect and diminished
Object: Within 2F ’ (or near object) O F 2F I 2F' F' C Image: Between F ’ and 2F ’, on the same side of object virtual, erect and diminished

Magnification F I C F' O magnification m height of image (image size)
ho hi magnification m height of image (image size) hi = = height of object (object size) ho

Also, F I C F' O image distance v magnification m =  m = u
Also see Simulation program 4.8 in Physics at Work Multimedia CD-ROM 1. image distance v magnification m =  m = u object distance

The Thin-Lens Equation

The Thin-Lens Equation
Sign conventions for thin lenses:

Defects in Lens Spherical Aberration – Peripheral rays and axial rays have different focal points (caused by spherical shape of the lens surfaces. causes the image to appear hazy or blurred and slightly out of focus. The spherical aberration is caused by the spherical shape of the lens surfaces, hence spherical aberration. The center remains more in focus than the edges of the image and the intensity of the edges falls relative to that of the center. This defect appears in both on-axis and off-axis image points

Defects in Lens Chromatic Aberration Blue light is refracted to the greatest extent followed by green and red light, a phenomenon commonly referred to as dispersion. A converging lens can be combined with a weaker diverging lens, so that the chromatic aberrations cancel. The combination – achromatic doublet Light is not monochromatic. Light of different wavelengths is brought to focus at different distances from the center of the lens. This occurs because the refractive index of a transparent isotropic material is greater for light of shorter wavelength than for light of longer wavelength.-dispersion.

Example An object of height 5 cm is placed at 15 cm from a convex lens of focal length 10 cm. Find the position and magnification of the image. C F' 2F F O 5 cm

Height of image = 10 cm Height of object = 5 cm 5 cm 5 cm I O F 2F F' C = 10 cm 5 cm m = 2

Alternatively, Image distance = 30 cm Object distance = 15 cm 5 cm
F 2F O F' C = 30 cm 15 cm m = 2

Q1 Which of the following...
Which of the following incident rays is mentioned in the construction rules? A F F’ B F F’ C F F’

Q2 Which of the following light…
Which of the following light rays is correct ? F’ F A B C

Q3 A boy holds a magnifying...
A boy holds a magnifying glass at arm’s length. He looks at a poster through the glass and sees a magnified erect image. What happens to the image if he moves the lens closer to his eyes?

Q3 A boy holds a magnifying...
What happens to the image if he moves the lens closer to his eyes? A It gets larger till it gets totally blurred at some distance. B It gets larger, keeping erect all the way. C It gets smaller and becomes totally blurred at some distance. D It gets smaller, keeping erect all the way.

Q4 If you can capture an image...
If you can capture an image of a doll on a screen using a lens, which of the following may NOT be correct? A The lens you use is a convex lens. B The image is magnified. C The image is real. D The image is erect.

Q7 Both convex and concave...
Both convex and concave lenses can produce _______ images, which must be _________ than the object if convex lenses are used. virtual larger

An object is positioned between F’ and 2F’ of convex lens.
Complete the rays. 2F' F’’ O F 2F (a) Locate the image. (b) Is it a virtual or a real image?

Example 6 (a) O 2F I F’’ F 2F' (b) It is a real image.

Example 7 An object is positioned between F ’ and 2F ’ from concave lens. Complete the rays. O F’’ F 2F 2F' (a) Locate the image. (b) Is it a virtual or a real image?

Example 7 (a) I O F 2F 2F' F’’ (b) It is a virtual image.