Lenses

Physics 202Professor Lee

CarknerLecture 21

Refraction

Lenses have focal lengths and real and virtual images, but their properties also depend on the index of refraction

It has two sides we have to account for

thin symmetric lenses two identical refracting surfaces placed back to

back

Lenses and Mirrors Mirrors produce virtual images on the opposite side from the

object

i is negative in both cases Mirrors produce real images on the same side as the object

i is positive in both cases If a mirror curves towards the object, f and r are positive (real

focus)

Real is positive, virtual is negative

Converging Lens

Rays initially parallel to the central axis are focused to the focal point after refraction

The focal point is on the opposite side from the incoming rays

Converging lenses produce images larger than the object

m = -i/p

Diverging Lens

Rays initially parallel to the central axis diverge after refraction, but can be traced back to a virtual focus

f is virtual and negative

Diverging lenses produce images smaller than the object

Lens Equations A thin lens follows the same equation as a mirror,

namely:1/f = 1/p + 1/i

1/f = (n-1) (1/r1 -1/r2) Where r1 and r2 are the radii of curvature of each

side of the lens (r1 is the side nearest the object)

For symmetric lenses r1 and r2 have opposite sign

Converging Lenses and Images

Objects in front of the focal point (nearer to the lens) produce virtual images on the same side as the object Image is virtual so i is negative

Objects behind the focal point (further from the lens) produce real images on the opposite side of the lens Image is real so i is positive

Diverging Lenses and Images

For either lens the location of images is the reverse of that for mirrors:

Real images have positive i, virtual images have negative i

1)

2)

Two Lenses

To find the final image we find the image produced by the first lens and use that as the object for the second lens

M = m1m2

We can approximate several common optical instruments as being composed of a simple arrangement of thin lenses In reality the lenses are not thin and may be

arranged in a complex fashion

DualLenses

Near Point How can you make an object look bigger

Increases angular size

The largest clear (unlensed) image of an object is obtained when it is at the near point (about 25 cm)

A converging lens will increase the angular diameter of an object

m = ’/

Magnifying Lens

If the object is inside the near point you can view it through a lens which will produce a virtual image outside of the near point

The magnification is:m = 25 cm /f

This is the size of the object seen through

the lens compared to its size at the near point

Magnifying Glass

Compound Microscope

The objective creates a real image focused at the focal point of the eyepiece

The magnification of the objective is m = -i/p i is very close to the distance between the lenses, s

The total magnification is the product of the magnification of each

M = (-s/fob)(25 cm/fey) where s is the distance between the focal point of the lenses (the

tube length) and f is the focal length

Microscope

Refracting Telescope

The rays coming in from infinity are refracted by the objective to create a real image at the common focal point

The total angular magnification of the

telescope depends on the ratio of the eyepieces

m = -fob/fey

Refracting Telescope

Newtonian Telescope

Telescopes The magnification of the telescope can be altered by

changing eyepieces Short focal length means more magnification

Limited by blurring effects of atmosphere

The largest practical refracting telescope has an objective with a diameter of about 1m The objective becomes so large it is hard to build and support

Next Time

Read: 35.1-35.5

For a plane mirror what is the sign of f, the type of image and the orientation of the image?

A) +, real, uprightB) +, virtual, uprightC) -, virtual, invertedD) No sign, virtual, uprightE) No sign, real, inverted

For a convex mirror what is the sign of f, the type of image and the orientation of the image?

A) +, real, uprightB) +, virtual, uprightC) -, virtual, invertedD) -, virtual, uprightE) + real, inverted

For a concave mirror (with object close to the mirror) what is the sign of f, the type of image and the orientation of the image?

A) +, real, uprightB) +, virtual, uprightC) -, virtual, invertedD) -, virtual, uprightE) +, real, inverted

For a concave mirror (with object far from the mirror) what is the sign of f, the type of image and the orientation of the image?

A) +, real, uprightB) +, virtual, uprightC) -, virtual, invertedD) -, virtual, uprightE) +, real, inverted