Answer to Question #287067 in Optics for monkey

Question

1. An object 6 cm tall is placed 9 cm in front of a concave mirror that has a focal length of 18cm. Round your answers to 2 decimal places.  

a) Calculate the image distance. [3 marks]

b) Calculate the image height. [2 marks]

Answer 1

(a) In this problem, we will use a concave mirror equation:

$$\dfrac 1f=\dfrac 1o+\dfrac1i,\\\space\\ i=\dfrac{of}{o-f}=\dfrac{(-9)(-18)}{(-9)-(-18)}=18\text{ cm}.$$

(b) From magnification, find the image height:

$$M=-\dfrac io=\dfrac{h_i}{h_o}→h_i=-\dfrac{h_oi}{o}=-\dfrac{6·18}{-9}=12\text{ cm}.$$