Physics 213General Physics

Lecture 16

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Last Meeting: Reflection and Refraction of Light

Today: Mirrors and Lenses

t

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Are the red and violet lights coming from the same raindrop?

Dispersion by drops of water. Red is bent the least so comes from droplets higher in the sky.

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Why is the sky blue? Why is the sunset orange?

hint

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Why is the cloud white?

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∞

12demo

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Funny Mirror

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Ray Diagram for Diverging Lens

The image is virtual The image is upright

QUICK QUIZ 23.4

A plastic sandwich bag filled with water can act as a crude

converging lens in air. If the bag is filled with air and placed under

water, is the effective lens (a) converging or (b) diverging?

QUICK QUIZ 23.4 ANSWER

(b). In this case, the index of refraction of the lens material is less than that of the surrounding medium.

Under these conditions, a biconvex lens will be divergent.

Image Example Between F’ and O

F’ FO

Behind lens, virtual, uprightlarger than object

Magnifying glass

F’ FO

At F’

No image Lighthouse

Between F’ and 2F’

F’ FO2F’

Beyond 2F, real, inverted, larger

Projector

F’ FO2F’

At 2F, real, inverted, same as object

Office copier

At 2F’

F’ FO2F’Between F and 2F,Real, inverted, smaller

Camera

Beyond 2F’

F’ O2F’

At F, real, inverted,smaller

F CameraAt infinity

Example: (a) An object 31.5 cm in front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this and what is its focal length? Is the image real or virtual? (b) If the image were located, instead, 38.0 cm in front of the lens, what type of lens would it be and what focal length would it have?

Solution: (a) 1/do+1/di=1/f where do=31.5 cm, di=-8.20 cm

1/31.5+1/(-8.20)=1/f, which yields f=-11.1 cm, thus

diverging lens. The image is in front of the lens, so it is virtual

(b) Similarly, we have 1/31.5+1/(-38.0)=1/f. which gives

f=+184 cm, thus, converging lens.

F’ FO

(b)

F ImageF’

(a)

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Question: An object infinitely far from a converging lens has an image that is

(a) real

(b) virtual

(c) upright

(d) larger than the object

Answer: a

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Question: An object farther from a converging lens than its focal point always has an image that is

(a) inverted

(b) virtual

(c) the same in size

(d) smaller in size

Answer: a

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Quiz: An object closer to a converging lens than its focal point always has an image that is

(a) inverted

(b) virtual

(c) the same in size

(d) smaller in size

Answer: b

Sign Conventions for Mirrors

1 1 2p q R

'

1 1 1

h qM

h p

p q f

Concave gives “+” conventions

Sign Conventions for Refracting Surfaces/Lenes

These are the same sign conventions – so just remember them for thin lenses.

1 2

1 1 1( 1)n

f R R

1

2

' n qhM

h n p

n1 is the source mediumn2 is the observing medium

Rnn

qn

pn 1221

'

1 1 1

h qM

h p

p q f

Combinations of Thin Lenses The image produced by the first lens is calculated as though the second lens

were not present The light then approaches the second lens as if it had come from the image of

the first lens The image of the first lens is treated as the object of the second lens The image formed by the second lens is the final image of the system If the image formed by the first lens lies on the back side of the second lens,

then the image is treated at a virtual object for the second lens p will be negative

The overall magnification is the product of the magnification of the separate lenses