Lenses

Physics 202Professor Lee

CarknerLecture 23

Refraction

Lenses can be used for the same purposes

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

Lenses

We will consider only thin lenses, i.e. thickness much smaller than i, p or f

If the two surfaces are the same, the lens is symmetric

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

object

Mirrors produce real images on the same side as the object

If a mirror curves towards the object, f and r are positive

(real focus)

Real is positive, virtual is negative

Converging and Diverging

Converging Lens

A lens consisting of two convex lenses back to back is called a converging lens

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

A lens consisting of two concave lenses back to back is called a diverging lens

f is virtual and negative

Diverging lenses produce images smaller than the object

Converging and Diverging

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

Three Types of Images

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

Objects behind the focal point (further from the lens) produce real images on the opposite side of the lens

Diverging Lenses and Images

No matter where the object is, a diverging lens produces an upright, virtual image on the same side as the object

Virtual images form on the same side as the object, real images form on the opposite side

Three Types of Images

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

For a two lens system the magnification is:M = m1m2

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

Magnifying Lens You can use a magnifying lens to overcome

the limitation of your eye’s 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 A simple compound microscope consists of an objective and

eyepiece

The eyepiece acts as a magnifying glass The magnification of the objective is m = -i/p

p is very close to the focal length of the objective, fob

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 In a telescope the two lenses are placed so

that the two inner focal points are in the same place

The eyepiece then magnifies the real image

m = -fob/fey

Refracting Telescope

Giant 40 inch Refractor at Yerkes

Observatory,Williams Bay

Wisconsin

Newtonian Telescope

Telescopes The magnification of the telescope can be altered by

changing eyepieces

Magnification is not the most important property of a telescope

The true purpose of the objective lens is to gather more light than your eye can and focus it so that it can be viewed

The objective becomes so large it is hard to build and support