Question

An object is placed $ 30\, cm $ in front of a convex lens of focal length $ 20\, cm $. Find the position of the image.

• A. \(60\, cm\)
• B. \(12\, cm\)
• C. \(15\, cm\)
• D. \(10\, cm\)

Hint:

Tip: Remember the sign conventions for lenses carefully when applying the lens formula.

Answer 1

The Correct Option is A

The position of the image formed by a convex lens is determined using the lens formula:

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

Where:

• \( f \) represents the focal length of the lens.
• \( v \) denotes the image distance from the lens.
• \( u \) signifies the object distance from the lens.

Given values:

• Focal length, \( f = 20\, \text{cm} \) (positive for a convex lens).
• Object distance, \( u = -30\, \text{cm} \) (negative convention for object distance).

Substituting these values into the lens formula:

\( \frac{1}{20} = \frac{1}{v} - \frac{1}{-30} \)

Simplifying and solving for \( v \):

\( \frac{1}{20} = \frac{1}{v} + \frac{1}{30} \)

\( \frac{1}{v} = \frac{1}{20} - \frac{1}{30} \)

Using a common denominator (60):

\( \frac{1}{v} = \frac{3}{60} - \frac{2}{60} \)

\( \frac{1}{v} = \frac{1}{60} \)

Therefore,

\( v = 60\, \text{cm} \)

The image is located \( 60\, \text{cm} \) from the lens.