Physics 222, October 24 - University of Tennesseelabman.phys.utk.edu › phys222 › PDF › P8.pdf · You’d like to look through a lens at your dog and see it standing right side

Physics 222, October 24

Key Concepts:

•Image formation by refraction•Thin lenses•The eye•Optical instruments

A single flat interfaceImages can be formed by refraction, when light traverses a boundary between twotransparent media with different indices of refraction.

When we are looking at an object under water, we are seeing a virtual image of theobject.

The treasure hunter on the boat observes

1. a real, magnified image of the chest.

2. a virtual, magnified image of the chest.

3. no image, but the chest itself.4. a real image of the chest, the

same size as the chest.5. a virtual image of the chest,

the same size as the chest.

A single spherical interfaceA single spherical interfaces with radius of curvature R can also act as a image forming system. Example:

(As R infinity, the interface becomes flat.)

Images formed by thin lenses

Thin lenses can be converging or diverging.

Where is the image located?Lens equation: 1/xo + 1/xi = 1/f , M = -xi/xo

Convention:• xo is positive. • xi is positive if xo and xi are on the opposite sides of the lens. • xi is negative if xo and xi are on the same side of the lens. • f is positive for a converging lens. • f is negative for a diverging lens.

Images formed by thin lenses

Geometrical construction:Real images

Virtual images

Diverging lenses only form virtual images.Converging lenses form real inverted images if xo > f and virtual upright images if xo < f.

Lens equation: 1/xo + 1/xi = 1/f, M = -xi/xo

Here are some things that always go together for a thin lens.

Real image <--> inverted image <--> xi is positive <--> M is negative

Virtual image <--> upright image <--> xi is negative <--> M is positive

Virtual image produced by converging lens <--> M > 1,(image is larger than object)

Virtual image produced by diverging lens <--> M < 1,(image is smaller than object)

An object is located a distance xo in front of a lens. The lens produces an inverted image that is four times as tall as the object.What kind of lens is it? What is the image distance, xi ?

1. Converging lens, xi = 2xo

2. Converging lens, xi = xo/43. Converging lens, xi = 4xo

4. Diverging lens, xi = -4xo

5. Diverging lens, xi = -xo/4

An object is placed at 20 cm in front of a diverging lens with a focal length of -10 cm. What is the image distance?

1. 6.67 cm behind the lens2. 0.15 cm in front of the lens3. 6.67 cm in front of the lens4. 0.1 cm in front of the lens5. 10 cm in front of the lens

You’d like to look through a lens at your dog and see it standing right side up shrunk to 1/3 its normal height. If the absolute value of the focal length is f, determine what kind of lens is needed (i.e. converging or diverging) as well as the focal length in term of the object distance xo.

1. Converging lens, f = xo/2.2. Diverging lens, f = -xo/2.3. Converging lens, f = xo/3.4. Diverging lens, f = -xo/3.5. Converging lens, f = xo/4.6. Diverging lens, f = -xo/4.

HintM = -xi/xo = 1/3

Lens power

Lens power P, measured in diopters D: D = 1/f(m)For two thin lenses in contact:1/f = 1/f1 + 1/f2

P = Pthin(1) + Pthin(2)

The powers of thin lenses in contact add algebraically.

Two very thin lenses, each with focal length 20 cm, are placed in contact. What is the focal length of this compound lens?

1. 7.5 cm2. 10 cm3. 25 cm4. 20 cm

The human eyeThe eye focuses an image onto the retina by adjusting the focal length of theeye lens. This is known as accommodation.

Normal eye:

1.60

1.70

1.80

1.90

2.00

0 20 40 60 80 100

foca

l len

gth

(cm

)

object distance (cm)

Eye: image distance = 2 cm

Your eye focuses on an moving motorcycle by changing its focal length. As the motorcycle moves away from you, the focal length of the eye must

A. increase.B. decrease.C. stay the same.

Hint:1/xo + 1/xi = 1/fxi is fixed.

Nearsighted eye

Farsighted eye

A person’s left eye is corrected by a 2.50-diopter lens, 1.0 cm from the eye. Is this person’s left eye near- or farsighted?

1. Nearsighted2. Farsighted

Simple image-forming optical instruments

One lens:

One lens + eye:

Simple image-forming optical instrumentsTwo lenses + eye:Keplerian telescope Galilean telescope

Angular magnification: M = -fo/fe

Compound microscope

MP = MPobjetive*Mpeypiece = -(g/fo)*(25cm/fe)

You want to build a Galilean telescope. You have two convex lenses and two concave lenses available. The larger lenses have focal lengths +100 cm and –100 cm respectively and the smaller lenses have focal lengths +10 cm and – 10 cm respectively. Which lenses should you use and how far apart should you place them? What is the angular magnification of your telescope?

1. +100 and – 100, 100 cm apart2. +100 and +10, 110 cm apart3. +100 and - 10, 110 cm apart4. +100 and – 10, 90 cm apart