Question

A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Answer 1

Focal length of the concave lens, \(f = −15\ cm\)
Image distance, \(v = −10\ cm\)
Using the lens formula:
\(\frac 1v-\frac 1u=\frac 1f\)

\(\frac 1u=\frac 1v-\frac 1f\)

\(\frac 1u=-\frac {1}{10}-\frac {1}{(-15)}\)

\(\frac 1u=-\frac {1}{10}+\frac {1}{15}\)

\(\frac 1u=-\frac {5}{150}\)
Object distance, \(u=-30\ cm\)
The negative sign for \(u\) indicates that the object is positioned \(30\ cm\) in front of the lens, as depicted in the accompanying ray diagram.