Week 12: Lenses and Mirrors 415
Problem 6.A fish’s eye has a focal length of 1 cm in water (which is just the distance from the lens to
the fish’s retina, of course). Is its focal length in air longer or shorter? Don’t just answer
with a guess – you need to make a complete argument based on the lens-maker’s formula
or Snell’s law directly, supported by pictures. Is the fish nearsighted or farsighted in air?
Conversely, if you open your eyes underwater (and have normal vision in air) are you
nearsighted or farsighted?Problem 7.Draw ray diagrams and derive the magnification for: The standard telescope and the
Galilean telescope (one with an eyepiece lens with a negative focal length). Show that
the latter permits one to view the final image at infinity erect insteadof inverted.Problem 8.Draw ray diagrams and derive the magnification for: The standard microscope (with
tube lengthℓ) and the “Galilean” microscope (one with an eyepiece lens with a negative
focal length). Show that the latter permits one to view the final image at infinity erect
instead of inverted.Problem 9.a) Draw a ray diagram for the simple magnifier, deriving its (angular) magnification
in the standard picture.
b) Solve for where one has to locate the object to form a virtual, erect image at the
near point of the eyexnpas viewed through the magnifier.
c) What is the overall (angular) magnification of the image now (with the image located
atxnp)?Problem 10.From the previous problem, you saw that if one places the object viewed with a simple
magnifier at a position that isn’t exactly at focal point of the lens, one can achieve a
slightly greater angular magnification (at the expense of having to use accomodation in
order to view the final image at the near point of the eye instead of at infinity). Both
the microscope and telescope above use the eyepiece lens as a simplemagnifier to view
a real image.
Based on your result, by roughly whatfractiondo you think you can increase their
effective magnification if you locate the final image at the near point of the eye? Note