a 6 cm object is 15 cm from a convex lens that has a focal length of 5 cm. what is the distance of the image…

Answer:

C. 7.50 cm

Explanation:

Step1: Identify the lens - formula

The thin - lens formula is $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance.

Step2: Substitute the given values

Given $f = 5$ cm and $d_o=15$ cm. Substitute into the formula: $\frac{1}{5}=\frac{1}{15}+\frac{1}{d_i}$.

Step3: Solve for $\frac{1}{d_i}$

$\frac{1}{d_i}=\frac{1}{5}-\frac{1}{15}$. Find a common denominator, which is 15. Then $\frac{1}{d_i}=\frac{3 - 1}{15}=\frac{2}{15}$.

Step4: Solve for $d_i$

Taking the reciprocal of both sides, $d_i=\frac{15}{2}=7.50$ cm.