In the figure, the image is viewed on a screen and is 13.5 mm tall. What is the focal length of the lens?

Question

Quizplus · Accepted Answer

We can use the thin lens equation: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, where $f$ is the focal length of the lens, $d_o$ is the object distance (distance from the object to the lens), and $d_i$ is the image distance (distance from the lens to the image). We are given that the image height is 13.5 mm, but we need to find $d_i$. We can use similar triangles to set up the equation:

$\frac{13.5	ext{ mm}}{d_i} = \frac{y}{f}$

where $y$ is the height of the object (which we don't know, but it will cancel out later). We can rearrange this equation to solve for $d_i$:

$d_i = \frac{13.5	ext{ mm}}{y}f$

Next, we can use the fact that the lens produces a real image (which we can see on the screen), so the image distance is negative. We can plug in the given values:

$-	ext{13 cm} = \frac{13.5	ext{ mm}}{y}f - 	ext{10 cm}$

Simplifying and solving for $f$ gives:

$f = \boxed{	extbf{(C) }+20.4	ext{ cm}}$

In the Figure, the Image Is Viewed on a Screen