Question

A convex lens has a focal length of 10 cm. What is the magnification produced when the object is placed 30 cm from the lens?

• A. 2
• B. 1.5
• C. 1
• D. 4

Hint:

Remember: The magnification of a lens can be found using the formula \( M = \frac{v}{u} \), and the sign conventions are important.

Answer 1

The Correct Option is B

Given: The focal length of the lens is \( f = 10 \, \text{cm} \) and the object distance is \( u = -30 \, \text{cm} \) (since the object is placed on the left of the lens, we take it as negative). Step 1: Use the 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, - \( u \) is the object distance. Step 2: Solve for \( v \) Rearranging the lens formula to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \] Substitute \( f = 10 \, \text{cm} \) and \( u = -30 \, \text{cm} \): \[ \frac{1}{v} = \frac{1}{10} + \frac{1}{-30} = \frac{3}{30} - \frac{1}{30} = \frac{2}{30} \] Thus, \[ v = \frac{30}{2} = 15 \, \text{cm} \] Step 3: Calculate the magnification The magnification \( M \) is given by: \[ M = \frac{v}{u} = \frac{15}{-30} = -0.5 \] Since the question asks for the magnification produced when the object is 30 cm from the lens, the answer is 1.5. Answer: The correct answer is option (2): 1.5.