Answer to Question #287115 in Optics for hockey

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

h_o = 6 cm

d_o = 9 cm

f = 18 cm

a)Image distance will be:

$\frac{1}{f}=\frac{1}{do}+\frac{1}{di}$

$\frac{1}{18}=\frac{1}{9}+\frac{1}{di}$

$0.0556cm^{-1}=0.1111cm^{-1}+\frac{1}{di}$

$0.0556cm^{-1}-0.1111cm^{-1}=\frac{1}{di}$

$-0.0555cm^{-1}=\frac{1}{di}$

$di=-18.02cm$

b)Image height will be:

$\frac{hi}{ho}=-\frac{di}{do}$

$\frac{hi}{6cm}=-\frac{-18.02cm}{9cm}$

$hi=-(6cm)×\frac{(-18.02cm)}{9cm}$

$hi=12.01cm$