Question

If an object in case (i) above is 20 cm from the lens and the screen is 50 cm away from the object, the focal length of the lens used is:

• A. 10 cm
• B. 16 cm
• C. 12 cm
• D. 20 cm

Hint:

Use the lens formula \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) to calculate the focal length of the lens when the object and image distances are given.

Answer 1

The Correct Option is B

The focal length of the lens is calculated using the lens formula:

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

where \(f\) represents the focal length, \(v\) is the image distance, and \(u\) is the object distance. Given an object distance \(u = -20\) cm (following the convention of negative object distance) and an image distance \(v = 70\) cm (calculated from the object being 50 cm from the screen, totaling 20 cm + 50 cm), we substitute these values into the lens formula:

\( \frac{1}{f} = \frac{1}{70} - \frac{1}{-20} \)

\( \frac{1}{f} = \frac{1}{70} + \frac{1}{20} \)

Finding a common denominator yields:

\( \frac{1}{f} = \frac{20 + 70}{1400} = \frac{90}{1400} \)

Consequently, \( f = \frac{1400}{90} = \frac{140}{9} \approx 15.56 \text{ cm} \)

Therefore, the focal length of the lens is determined to be 16 cm.