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. 12 cm
• C. 16 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

We can use the lens formula to find the focal length of the lens: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( u = -20 \, \text{cm} \) (object distance), \( v = 50 \, \text{cm} \) (image distance). Substituting the values into the lens formula: \[ \frac{1}{f} = \frac{1}{50} - \frac{1}{-20} = \frac{1}{50} + \frac{1}{20} = \frac{2 + 5}{100} = \frac{7}{100} \] Thus: \[ f = \frac{100}{7} = 12 \, \text{cm} \] The focal length of the lens is \( 12 \, \text{cm} \).