A dentist uses a spherical mirror of radius 30cm to examine a tooth. The mirror is adjusted so that the image of the tooth is erect and 1.5 times the actual size of the tooth.
Answer the following questions:
(i) Derive an expression for the object distance u (in terms of the focal length f) when the linear magnification is a positive quantity m(m>0).
(ii) Using R=30cm and m=1.5, calculate the position of the tooth (object) and the position of its image with respect to the mirror.
(iii) Comment on the nature of the image produced in this situation and explain why such an image is suitable for dental examination.