Answer
a. 2.0 cm.
b. 1.9 cm.
Work Step by Step
a. Use the lens equation. The object is at infinity, and the image falls on the retina. This means that the image distance is 2.0 cm. The image is real, so the image distance is positive.
$$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{2.0cm}$$
$$ d_{i}=f= 2.0cm$$
b. Use the lens equation. Again the image distance is 2.0 cm, and now the object distance is 38 cm.
$$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$
$$f=\frac{d_o d_i}{d_o+d_i}=\frac{(34cm)(2.0cm)}{34cm+2.0cm}=1.9cm$$
