Question

18. You’re using a concave lens with f = -5.1 cm to read 5.0 mm high newspaper type.

Part A How high do the type characters appear if you hold the lens 1.4 cm from the newspaper?

Part B

How high do the type characters appear if you hold the lens 3.4 cm from the newspaper?

Part C

How high do the type characters appear if you hold the lens 12 cm from the newspaper?

Answer 1

We can use the lens equation:

do If

and the magnification equation:

$M=\frac{h_{i}}{h_{o}}=-\frac{d_{i}}{d_{o}}$

Part A: If the lens is 1.4 cm away from the newspaper

$d_{o}(\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}})\rightarrow \frac{d_{o}}{f}=\frac{d_{o}}{d_{o}}+\frac{d_{o}}{d_{i}}$

do 1

Now, solving for M:

$\frac{1}{M}=1-\frac{d_{o}}{f} \rightarrow M=\frac{1}{1-\frac{d_{o}}{f}}=\frac{f}{f-d_{o}}$

$M=\frac{-5.1 [cm]}{-5.1 [cm]-1.4 [cm]}=0.785$

Now, solving for $h_{i}$;

$M=\frac{h_{i}}{h_{o}}\rightarrow h_{i}=0.785 \cdot 5.0 [mm]=3.92 [mm]$

Part B: If the lens is 3.4 cm away from the newspaper

Using the previous equations

$M=\frac{f}{f-d_{o}}=\frac{-5.1 [cm]}{-5.1 [cm]-3.4 [cm]}=0.4$

$M=\frac{h_{i}}{h_{o}}\rightarrow h_{i}=0.4 \cdot 5.0 [mm]=2.0 [mm]$

Part C: If the lens is 12 cm away from the newspaper

Using the previous equations

$M=\frac{f}{f-d_{o}}=\frac{-5.1 [cm]}{-5.1 [cm]-12 [cm]}=0.298$

$M=\frac{h_{i}}{h_{o}}\rightarrow h_{i}=0.298 \cdot 5.0 [mm]=1.49 [mm]$