Lenses Physics 202 Professor Lee Carkner Lecture 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/r 1 -1/r 2 )  Where r 1 and r 2 are the radii of curvature of each side of the lens (r 1 is the side nearest the object)   For symmetric lenses r 1 and r 2 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 = m 1 m 2   In reality the lenses are not thin and may be arranged in a complex fashion

Dual Lenses

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, f ob  M = (-s/f ob )(25 cm/f ey )  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  = -f ob /f ey

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 