To determine the focal length we will use the following formula:
[tex]\frac{1}{d_0}+\frac{1}{d_i}=\frac{1}{f}[/tex]Where:
[tex]\begin{gathered} d_0=\text{ distance of the object} \\ d_i=\text{ distance of the image} \\ f=\text{ focal length} \end{gathered}[/tex]Now, we solve for "f". To do that we will add the fractions on the left side:
[tex]\frac{d_i+d_0}{d_0d_i}=\frac{1}{f}[/tex]Now, we invert both sides:
[tex]\frac{d_0d_i}{d_i+d_0}=f[/tex]Substituting the values:
[tex]\frac{(17cm)(5.2cm)}{17m+5.2cm}=f[/tex]Solving the operations:
[tex]3.98cm=f[/tex]Therefore, the focal length is 3.98 cm.
The focal length and the radius are related by the following formula:
[tex]r=2f[/tex]Where "r" is the radius. Substituting the value we get:
[tex]r=2(3.98cm)[/tex]Solving the operations:
[tex]r=7.96cm[/tex]Therefore, the radius of curvature is 7.96 cm.
