Question

The distance between object and its two times magnified real image as produced by a convex lens is 45 cm. The focal length of the lens used is ______ cm.

Answer 1

Correct Answer: 10

Step 1. Understanding the Given Condition: Since the image is real, inverted, and twice the size of the object, we know:

\( m = \frac{v}{u} = -2 \Rightarrow v = -2u \)

Step 2. Set up Equation Using Total Distance: The distance between the object and the image is 45 cm, so:

\( |v - u| = 45 \, \text{cm} \)

Substitute \( v = -2u \) into the equation:

\( |-2u - u| = 45 \)

\( 3|u| = 45 \Rightarrow u = -15 \, \text{cm} \)

Step 3. Determine Image Distance \( v \): Using \( v = -2u \):

\( v = -2 \times (-15) = 30 \, \text{cm} \)

Step 4. Calculate Focal Length Using Lens Formula: Apply the lens formula:

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

Substitute \( u = -15 \, \text{cm} \) and \( v = 30 \, \text{cm} \):

\( \frac{1}{f} = \frac{1}{30} - \frac{1}{-15} = \frac{1}{30} + \frac{1}{15} = \frac{1 + 2}{30} = \frac{3}{30} = \frac{1}{10} \)

\( f = +10 \, \text{cm} \)