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

To find the position of the image formed by a convex lens, we use the lens formula:

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

Where:

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

Given:

• Focal length, \( f = 20\, \text{cm} \) (convex lens, so \( f \) is positive).
• Object distance, \( u = -30\, \text{cm} \) (object distance is taken negative in lens formula).

Substitute values into the lens formula:

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

Simplify and solve for \( v \):

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

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

Find a common denominator (60 in this case):

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

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

Thus,

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

The image is formed at a distance of \( 60\, \text{cm} \) from the lens.

Answer 2

Step 1: Write down known values 
Object distance, \( u = -30\, cm \) (object distances are negative in lens formula convention)
Focal length, \( f = 20\, cm \)

Step 2: Use lens formula 
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( v \) is image distance.

Step 3: Substitute and solve for \( v \) 
\[ \frac{1}{20} = \frac{1}{v} - \frac{1}{-30} = \frac{1}{v} + \frac{1}{30} \] \[ \frac{1}{v} = \frac{1}{20} - \frac{1}{30} = \frac{3 - 2}{60} = \frac{1}{60} \] \[ v = 60\, cm \]