Question

An object is placed at a distance of $ 30 \, cm $ from a concave lens of focal length $ 20 \, cm $. The image distance is:

• A. \( 75 \, cm \)
• B. \( 60 \, cm \)
• C. \( 12 \, cm \)
• D. \( 50 \, cm \)

Hint:

For concave lenses, focal length is negative, and virtual images have negative image distances.

Answer 1

The Correct Option is C

Step 1: Identify the given values and sign conventions.
Object distance \( u = -30 \, cm \) (concave lens) Focal length \( f = -20 \, cm \) (concave lens) We need to find the image distance \( v \).
Step 2: Apply the lens formula.
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Step 3: Substitute the values and solve for \( v \).
\[ \frac{1}{-20} = \frac{1}{v} - \frac{1}{-30} \] \[ -\frac{1}{20} = \frac{1}{v} + \frac{1}{30} \] \[ \frac{1}{v} = -\frac{1}{20} - \frac{1}{30} = -\frac{3}{60} - \frac{2}{60} = -\frac{5}{60} = -\frac{1}{12} \] \[ v = -12 \, cm \] The image distance is \( -12 \, cm \), indicating a virtual image on the same side as the object. The magnitude is \( 12 \, cm \).