Question

a 6 cm object is 8 cm from a convex lens that has a focal length of 2.7 cm. the image is 4 cm from the lens. the height of the image is cm.

Explanation:

Step1: Use magnification formula

The magnification formula is \(m=\frac{h_{i}}{h_{o}}=\frac{v}{u}\), where \(h_{i}\) is image height, \(h_{o}\) is object height, \(v\) is image distance, \(u\) is object distance.

Step2: Substitute values

Given \(h_{o} = 6\space cm\), \(u=8\space cm\), \(v = 4\space cm\). Substitute into \(\frac{h_{i}}{h_{o}}=\frac{v}{u}\), we get \(\frac{h_{i}}{6}=\frac{4}{8}\).

Step3: Solve for \(h_{i}\)

Cross - multiply: \(8h_{i}=6\times4\), so \(h_{i}=\frac{6\times4}{8}=3\space cm\).

Answer:

3