Optical instruments
1. A camera with a shutter
speed of 0.01 s and a lens of focal length 50 mm is used to photograph a car
100 m away and moving at 50 m s-1 perpendicular to the line of
sight. By how much will the image on the film be blurred?
2. The telephoto lens
system of a camera consists of two lenses: a convex lens of focal length 12 cm
mounted 4 cm in front of a concave tens of focal length 10 cm. How much larger
will the image of a distant object be if the telephoto lens system is used
compared with the image produced by the convex lens alone?
3.
When an astronomical telescope is used to view a star the distance between the
objective and the eyepiece is 75 cm. When used to view a flagpole the eyepiece
has to be pulled out 2 cm to give a clearly focused image. If the focal length
of the eyepiece is 5 cm, what is the distance of the pole from the objective?
If
the image subtends an angle of 10° at
the eyepiece, find the height of the pole. (Assume that the final image is at
infinity in each case.)
4.
An astronomical telescope has an objective with a focal length of 100 cm and a
diameter of 5 cm. If the eyepiece has a focal length of 20 cm and the
telescope is used in normal adjustment, calculate
(a) the magnifying power,
(b) the diameter of the eye ring, and
(c) the separation of the lenses.
5.
The Moon subtends an angle of 0.5° at
the Earth's surface. What is the diameter of the image of the Moon produced by
the 102 cm Lick Observatory refractor, which has a focal length of 18 m?
Calculate
the resolving power of this instrument when light of wavelength 600 nm is used.
6.
A certain Cassegrain reflector with a main mirror of focal length 6 m is used
to view a planet such that the final image formed by the mirrors is at the pole
of the concave mirror. It is viewed there by means of an eyepiece lens of focal
length 7.5 cm. The distance between the poles of the mirrors is 5.5 m and the
angular diameter of the planet when viewed without a telescope is 10-4
radian. Calculate
(a) the diameter of the real image formed by the
mirrors,
(b) the magnifying power of the telescope when in
normal adjustment, and
(c) the magnifying power when the final virtual
image is formed 25 cm from the eyepiece.
7.
(a) An astronomer has two telescopes of the same magnifying power but of
different apertures. Discuss the advantages and disadvantages of each.
(b) What would be the result of using a back-silvered
mirror as the flat in a Newtonian reflecting telescope?
(c) Describe with the aid of a labelled diagram
the structure and purpose of a Schmidt telescope.
8.
Two thin convex lenses are used to form a compound microscope. An object 3 cm
in front of the objective lens gives a final image at the same position as the
object and 25 cm from the eye lens, the magnification being 15.
Calculate
the focal lengths of both the objective lens and the eye lens.
9.
A compound microscope is formed from two convex lenses, an eyepiece of focal
length 5.0 cm and an objective of focal length 1.0 cm. If an object is placed
1.1 cm from the objective, the final image is formed 32.0 cm from the eye lens.
Calculate
the magnifying power of the instrument if the near point is 25 cm from the
observer's eye.
