## Friday, 5 September 2014

### OPTICAL INSTRUMENTS

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.