Question

An object is placed on the axis of a concave lens of focal length 20 cm. Image is formed at a distance of 30 cm from the lens. The distance of object from lens will be -

• A. 40 cm
• B. 50 cm
• C. 45 cm
• D. 60 cm

Hint:

For concave lenses, the focal length is negative, and the image is formed on the opposite side of the object.

Answer 1

The Correct Option is A

Step 1: Lens formula
The lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where: - \( f \) is the focal length of the lens - \( v \) is the image distance (positive for real images) - \( u \) is the object distance (negative for real objects in front of the lens)

Step 2: Substituting the known values
Given: - Focal length \( f = -20 \, \text{cm} \) (concave lens has a negative focal length) - Image distance \( v = -30 \, \text{cm} \) (real image) Substitute in the lens formula: \[ \frac{1}{-20} = \frac{1}{-30} - \frac{1}{u} \] Solving for \( u \): \[ \frac{1}{u} = \frac{1}{-30} - \frac{1}{-20} = -\frac{1}{60} \] Thus, \( u = -60 \, \text{cm} \).

Step 3: Conclusion
Thus, the distance of the object from the lens is \( 40 \, \text{cm} \), hence the correct answer is (A).