Respuesta :
ANSWER:
The mirror’s magnification is 0.06
The focal length is equal to 19.15 cm.
The mirror's radius of curvature is 38.3 cm
STEP-BY-STEP EXPLANATION:
Given:
height image = 9 cm
height object = 1.5 m = 150 cm
The mirror's magnification is calculated using the following formula:
[tex]m=\frac{h_i}{h_o}=\frac{9}{150}=0.06[/tex]The mirror’s magnification is 0.06
Since we know the distance of the object which is -3 m (-300 cm) and the mirror's magnification we can calculate the distance of the image, just like this:
[tex]\begin{gathered} m=\frac{-d_i}{d_o} \\ \\ 0.06=\frac{-d_i}{-300} \\ \\ d_i=300\cdot0.06 \\ \\ d_i=18\text{ cm} \end{gathered}[/tex]We calculate the focal length using the following formula:
[tex]\begin{gathered} \frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o} \\ \\ \frac{1}{f}=\frac{1}{18}+\frac{1}{-300} \\ \\ \frac{1}{f}=\frac{18-300}{-5400} \\ \\ f=\frac{-5400}{-282} \\ \\ f=\:19.15\text{ cm} \end{gathered}[/tex]The focal length is equal to 19.15 cm.
Finally we calculate the mirror's radius of curvature knowing that twice the focal length, therefore:
[tex]\begin{gathered} r=2f=19.15\cdot2 \\ \\ r=38.3\text{ cm} \end{gathered}[/tex]The mirror's radius of curvature is 38.3 cm
