a 5.0 cm object is 6.0 cm from a convex lens, which has a focal length of 7.0 cm. what is the distance of…

Explanation:

Step1: Use thin - lens formula

The thin - lens formula is $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance. Given $f = 7.0\ cm$ and $d_o=6.0\ cm$. We can rewrite the formula for $d_i$ as $\frac{1}{d_i}=\frac{1}{f}-\frac{1}{d_o}$. Substitute the values: $\frac{1}{d_i}=\frac{1}{7}-\frac{1}{6}=\frac{6 - 7}{42}=-\frac{1}{42}$. So, $d_i=-42\ cm$.

Step2: Use magnification formula for height

The magnification formula is $m =-\frac{d_i}{d_o}=\frac{h_i}{h_o}$, where $h_i$ is the image height and $h_o$ is the object height. We know $h_o = 5.0\ cm$, $d_o = 6.0\ cm$, and $d_i=-42\ cm$. First, $m=-\frac{-42}{6}=7$. Then, since $m=\frac{h_i}{h_o}$, we can solve for $h_i$: $h_i=m\times h_o$. Substitute the values: $h_i = 7\times5=35\ cm$.

Answer:

-42 35