Question

An object placed 37.5 cm in front of a 15.0-cm focal length convex lens produces an image that is 25.0 cm away from the lens. a) calculate the magnification of the image. b) If the image has a height of -3.56 cm, calculate the object's height.

Answer 1

ANSWER:

a. -0.67

b. 5.3 cm

STEP-BY-STEP EXPLANATION:

Given:

Distance of object = 37.5 cm

Focal length = 15 cm

Distance of image = 25 cm

a.

We can calculate the magnification as follows:

$\begin{gathered} M=-\frac{d_i}{d_o} \\ \text{ we replacing} \\ M=-\frac{25}{37.5} \\ M=-0.67 \end{gathered}$

b.

Knowing the magnification we can calculate the height of the object, just like this:

$\begin{gathered} M=\frac{h_i}{h_o} \\ \text{ We replacing} \\ -0.67=\frac{-3.56}{h_o} \\ h_o=\frac{-3.56}{-0.67} \\ h_o=5.3cm \end{gathered}$