Answer to Question #285514 in Optics for TPB

Question

 1. A convex mirror has a focal length of -0.90 m. An object with a height of 0.40 m is 2.5 m from the mirror. a) Calculate the image distance b) Calculate the image height.

Answer 1

Solution:

$\begin{aligned} &\text {(a): Given: } f=-0.90 \mathrm{~m}, h_{0}=0.40 \mathrm{~m}, d_{0}=2.5 \mathrm{~m} \\ & d_{i}=? \\ &\frac{1}{d_{i}}=\frac{1}{f}-\frac{1}{d_{0}} \\ & \frac{1}{d_{i}}=\frac{1}{-0.90}-\frac{1}{2.5} \\ &d_{i}=-0.66 \mathrm{~m} \\ &\therefore d_{i} \text { is }-0.66 \mathrm{~m} \\ &(b): Given: f=-0.90 \mathrm{~m}, h_{0}=0.40 \mathrm{~m}, d_{0}=2.5 \mathrm{~m}, d_{i}=-0.66 \mathrm{~m} \\ & h_{i}=? \\ & h_{i}=\frac{-d_{i} h_{0}}{d_{0}} \\ & h_{i}=-\frac{(-0.66)(0.40)}{(2.5)} \\ &\quad=0.11 \mathrm{~m} \\ & \therefore h_{i} \text { is }+0.11 \mathrm{~m} \end{aligned}$