Question

a 14 cm object is 20 cm from a concave lens that has a focal length of -10 cm. the distance of the image from the lens, rounded to the nearest tenth, is cm.

Explanation:

Step1: Recall the lens formula

The lens formula is \(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\), where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance.

Step2: Substitute the given values

Given \(f=- 10\space cm\) and \(u = - 20\space cm\) (object distance is negative for a concave lens).
Substituting into the formula \(\frac{1}{-10}=\frac{1}{v}-\frac{1}{-20}\).

Step3: Solve for \(v\)

First, rewrite the equation: \(\frac{1}{v}=\frac{1}{-10}-\frac{1}{20}\).
Find a common denominator: \(\frac{1}{v}=\frac{-2 - 1}{20}=\frac{-3}{20}\).
Then \(v=-\frac{20}{3}\approx - 6.7\space cm\).

Answer:

\(-6.7\)