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:
Show Hint
- 10 cm
16 cm
12 cm
- 20 cm
The Correct Option is B
Solution and Explanation
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.
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