a 14 cm object is 20 cm from a concave lens that has a focal length of -10 cm. the distance of the image…

Explanation:

Step1: Use thin - 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. Given $f=- 10$ cm and $d_o = 20$ cm. Substitute the values into the formula: $\frac{1}{-10}=\frac{1}{20}+\frac{1}{d_i}$.

Step2: Solve for $\frac{1}{d_i}$

$\frac{1}{d_i}=\frac{1}{-10}-\frac{1}{20}$. Find a common denominator: $\frac{1}{d_i}=\frac{-2 - 1}{20}=\frac{-3}{20}$.

Step3: Solve for $d_i$

Take the reciprocal of both sides: $d_i=-\frac{20}{3}\approx - 6.7$ cm.

Answer:

$-6.7$