a 24.8 cm tall object is placed in front of a lens, which creates a -3.09 cm tall image. if the object is…

Explanation:

Step1: Recall magnification formula

The magnification formula is $m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}$, where $h_i$ is the height of the image, $h_o$ is the height of the object, $d_i$ is the image - distance and $d_o$ is the object - distance.

Step2: Calculate the magnification

Given $h_o = 24.8$ cm and $h_i=-3.09$ cm. First, calculate the magnification $m$ using $m=\frac{h_i}{h_o}$. So, $m=\frac{-3.09}{24.8}\approx - 0.125$.

Step3: Solve for the image distance

We know that $m =-\frac{d_i}{d_o}$, and $d_o = 37.5$ cm. Since $m=-0.125$, we can rewrite the formula as $-0.125=-\frac{d_i}{37.5}$. Cross - multiply to get $d_i=0.125\times37.5$. $d_i = 4.6875$ cm.

Answer:

$4.69$ cm (rounded to two decimal places)