Chapter 34: Thin Lenses

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Now consider refraction through this piece of glass:

opticaxis

This is called a “Double Convex Lens”

converging light

focal point

refraction occurs here

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Converging Lenses(convex)

Diverging Lenses(concave)

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Converging Lens

The focal point is visible because real rays go through it.

Diverging Lens

Where is the focal point for these 4 incoming rays?

Don’t confuse these reflections for something meaningful.

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Optical Ray Diagram: a line drawing depicting a small number of key light rays. For a lens, an optical ray diagram should include:

1. Parallel Ray. A ray parallel to the optic axis which passes through the object & the focal point.

2. Focal Ray. A ray that passes through both the focal point and the object.

3. Chief Ray. A ray that passes through both the center of the lens and the object.

These three rays intersect at the image.Note: we don’t use reflected rays in lens analysis.

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The Diverging Lens

parallel ray

virtual p

art

real p

art

Virtual part: where the refracted ray appears to come from.

f f

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The Diverging Lens

virtual part real part

focal ray

Virtual part: where the refracted ray appears to come from.

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The Diverging Lens

chief ray

The chief ray has no virtual part.

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Put all three rays together:

The three refracted rays have no intersection.

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Put all three rays together:

There is an intersection of the virtual parts.

Need virtual parts to find the image? Virtual image.

upright image

object

focalpoint

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Parallel ray

Chief rayFocal ray

so

f

si

a converging lens

The Thin Lens Equation

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Parallel ray

Chief rayFocal ray

a converging lens

Positive side forobject distance

Negative side forimage distancefocal length (e.g. diverging lens)

Positive side forimage distancefocal length

Opposite for mirrors

The Thin Lens Equation

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fss io

111

The Thin Lens Equation

“Strength” or “Power” of lens

fP

1

f, so and di all must have the same length units.

Units of P usually in [m-1] or rather [Diopters].

Pss io

11

Note: our book uses “P”. Other books use “S”.

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Why is 1/f called the “lens power”?

focal point at

light on the EFFECT NO has lens then the

0 f

1Prather or f if

(or sometimes “strength”)

“approaches”

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focal point very close to the lens

light on the EFFECT HUGE A has lens then the

f

1Prather or 0f if

Why is 1/f called the “lens power”?(or sometimes “strength”)

“approaches”

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Example 1: A lens focuses light from an object 2.75m away as an image 0.483m on the other side of the lens. What are the focal length, lens type and image type?

The lens is converging because: f>0

Converging lens: f>0Diverging lens: f<0

What is the image type?

meters 411.0

483.0

1

75.2

1111

f

mmssf io

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The image is real (si>0). Is it inverted or upright?

Ray diagram shows the image is: Real Inverted

True whenever the object is outside the focal point of a converging lens.

2.75 m

0.411m

0.483m

6 cm = 1m

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The ray diagram also shows the image is small.

hohi

Magnification:

o

i

o

i

d

d

h

hm

Minus sign indicates that real images are always inverted.

positive side for di and f

negative side for di and f

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How to do lens problems graphically

1. Use a full sheet – Landscape.2. Sketch the lens on the optic axis.3. Sketch the objects – correctly positioned.4. Show a scale. You might wish to show a

different scale for vertical and horizontal lengths

5. Sketch two principle rays per object and find the image.

6. Refraction occurs on the vertical center-line.

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Example 2: How far from a converging lens with a focal length of 25 cm should an object be placed to produce a real image which is the same size as the object?

cm 50s

s

2

s

1

s

1

cm 25

1

s

1

s

1

f

1

ooo

io

o

oss 1 s

s m want We i

o

i (Minus because all real images are inverted.)

si >0

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How to make a magnifying glass

What kind of lens has an upright image with m>1?

si <0

f

Place the object within the focal length of a converging lens.

1o

i

s

sm si negative

|si| > |so| image is farther from the

lens than the object