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

To find the focal length of the lens, we use the lens formula:

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

where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance. Given that the object distance \(u = -20\) cm (convention: object distance is negative) and the screen is 50 cm away from the object, the image distance \(v = 20 + 50 = 70\) cm. 

Substitute these values into the lens formula:

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

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

Convert to a common denominator:

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

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

So, the focal length of the lens is 16 cm.