In order to find the distance from the image to the lens, we can use the formula below:
[tex]\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}[/tex]Where f is the focal length (in m), do is the object distance and di is the image distance.
So, using f = 0.3 m and do = 4di, we have:
[tex]\begin{gathered} \frac{1}{0.3}=\frac{1}{4d_i}+\frac{1}{d_i}\\ \\ \frac{1}{0.3}=\frac{1+4}{4d_i}\\ \\ \frac{1}{0.3}=\frac{5}{4d_i}\\ \\ 4d_i=5\cdot0.3\\ \\ 4d_i=1.5\\ \\ d_i=\frac{1.5}{4}\\ \\ d_i=0.375\text{ m} \end{gathered}[/tex]Therefore the distance from the image to the lens is 37.5 cm.
