Lenses Physics 202 Professor Lee Carkner Lecture 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/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

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 = m 1 m 2  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

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 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/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   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  = -f ob /f ey

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:

For a plane mirror what is the sign of f, the type of image and the orientation of the image? A)+, real, upright B)+, virtual, upright C)-, virtual, inverted D)No sign, virtual, upright E)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, upright B)+, virtual, upright C)-, virtual, inverted D)-, virtual, upright E)+ 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, upright B)+, virtual, upright C)-, virtual, inverted D)-, virtual, upright E)+, 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, upright B)+, virtual, upright C)-, virtual, inverted D)-, virtual, upright E)+, real, inverted