Question

A convex lens has a focal length of \( 20 \, \text{cm} \). An object is placed at a distance of \( 30 \, \text{cm} \) from the lens. What is the position of the image formed?

• A. \( 60 \, \text{cm} \)
• B. \( 15 \, \text{cm} \)
• C. \( 10 \, \text{cm} \)
• D. \( 25 \, \text{cm} \)

Hint:

To find the position of the image in lens problems, use the lens formula \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) and solve for the image distance \( v \).

Answer 1

The Correct Option is A

We are given a convex lens with a focal length \( f = 20 \, \text{cm} \) and an object placed at a distance of \( u = -30 \, \text{cm} \) (object distance is always negative for real objects). We are asked to find the position of the image formed. Step 1: Use the lens formula The lens formula relates the object distance (\( u \)), the image distance (\( v \)), and the focal length (\( f \)): \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Rearranging to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \] Step 2: Substitute the known values Substitute the given values into the lens formula: \[ \frac{1}{v} = \frac{1}{20} + \frac{1}{-30} \] \[ \frac{1}{v} = \frac{1}{20} - \frac{1}{30} \] To simplify, take the least common denominator (LCD) of 20 and 30, which is 60: \[ \frac{1}{v} = \frac{3}{60} - \frac{2}{60} = \frac{1}{60} \] Step 3: Solve for \( v \) \[ v = 60 \, \text{cm} \] Step 4: Conclusion The image is formed at a distance of \( 60 \, \text{cm} \) on the opposite side of the object, indicating a real and inverted image. Answer: The position of the image is \( 60 \, \text{cm} \), so the correct answer is option (1).