Q58E - University Physics with Modern Physics

Question

You want to view through a magnifier an insect that is 2.00 mm long. If the insect is to be at the focal point of the magnifier, what focal length will give the image of the insect an angular size of 0.032 radian?

Step-by-Step Solution

Answer

The focal length of the magnifier should be 6.25 cm.

Step 1: Relation between original height of the object, focal length of the lens and angular size of the image

$f=\frac{y}{{\theta }^{\text{'}}}$

Where f = focal length of the lens

             y = Original height of the object

            ${\theta }^{\text{'}}$= Angular size of the image

Step 2: Calculate the focal length

 $$\begin{gathered} f=\frac{y}{{\theta }^{\text{'}}} \\ \Rightarrow f=\frac{2mm}{0.032radian} \\ =6.25 \end{gathered}$$

 

Thus, the focal length of the magnifier is 6.25 cm.