Question

A convex lens has a focal length of \(20\,cm\). An object is placed \(30\,cm\) from the lens. The image distance is

• A. \(60\,cm\)
• B. \(30\,cm\)
• C. \(20\,cm\)
• D. \(15\,cm\)

Hint:

Lens Formula: \[ \boxed{\frac{1}{f}=\frac{1}{v}-\frac{1}{u}} \] For a convex lens: \[ \boxed{f>0} \] Always use the Cartesian sign convention.

Answer 1

The Correct Option is A

Step 1: Recall the lens formula. \[ \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \] Given: \[ f=+20\,cm \] \[ u=-30\,cm \]

Step 2: Substitute the values. \[ \frac{1}{20} = \frac{1}{v} + \frac{1}{30} \] \[ \frac{1}{v} = \frac{1}{20} -\frac{1}{30} \] \[ \frac{1}{v} = \frac{3-2}{60} = \frac{1}{60} \] \[ v=60\,cm \]

Step 3: Choose the correct option. \[ \boxed{v=60\,cm} \] Therefore, \[ \boxed{\text{(A)}} \] is the correct answer.