(a) Define the following terms as applied to a convex mirror:
(i) principal focus; (ii) pole (iii) radius of curvature.
(b) State one advantage and one disadvantage of using a convex mirror as a driving mirror.
(c) Draw a clearly labelled diagram to illustrate how two converging lenses may be arranged to form a compound microscope.
(d) An object 2.5 mm long is viewed through a converging lens of focal length 10.0 cm held close to the eye. A magnified image of the object is formed 30.0 cm from the lens. Calculate the:
(i) distance of the object from the lens; (ii) size of the image; (iii) power of the lens.
Explanation
(a)(i) Principal focus of a convex mirror is a pc.nt on the principal axis on which all rays parallel and close to the principal axis appear to diverge after reflection.
(ii) The pole is the centre of the mirror through which the principal axis pass.
(iii) Radius of curvature is the radius of the sphere from which the mirror was cut.
(b) Advantages of using convex mirror for driving
-wide field of view
-image is always upright.
Disadvantages of using convex for driving:
-image is smaller
-image appears further away and gives false impression of the distance.
(d)(i) \(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}; \frac{1}{u} - \frac{1}{30} = \frac{1}{10}; \frac{1}{u} = \frac{1}{10} + \frac{1}{30}\)
= \(\frac{4}{30} = \frac{2}{15}; u = \frac{15}{2}\) = 7.5cm
(ii) \(\frac{\text{image size}}{\text{object size}} = \frac{\text{image distance x object size}}{\text{object distance}}\)
= \(\frac{30 \times 0.25}{7.5} = 1cm\)
(iii) Power = \(\frac{1}{\text{focal length (in metre)}} = \frac{1}{0.1}\)
= +10.0 dioptre 0.1