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. 3
• C. 1.5
• D. 4

Hint:

Remember: For a convex lens, the magnification is the ratio of the image distance to the object distance. The image formed by a convex lens is real and inverted if the object is placed beyond the focal length.

Answer 1

The Correct Option is A

Step 1: Use the lens formula The lens formula relates the object distance (\( u \)), image distance (\( v \)), and focal length (\( f \)): \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Step 2: Use the magnification formula The magnification (\( M \)) produced by the lens is given by: \[ M = \frac{\text{Image height}}{\text{Object height}} = \frac{v}{u} \] Step 3: Substitute the given values into the lens formula Given: - \( f = 10 \, \text{cm} \), - \( u = -30 \, \text{cm} \) (object distance is always negative in lens formula). Now, use the lens formula to find \( v \): \[ \frac{1}{10} = \frac{1}{v} - \frac{1}{-30} \] \[ \frac{1}{10} = \frac{1}{v} + \frac{1}{30} \] \[ \frac{1}{v} = \frac{1}{10} - \frac{1}{30} = \frac{3 - 1}{30} = \frac{2}{30} = \frac{1}{15} \] \[ v = 15 \, \text{cm} \] Step 4: Calculate the magnification Now, use the magnification formula: \[ M = \frac{v}{u} = \frac{15}{-30} = -\frac{1}{2} \] The negative sign indicates that the image is inverted. Answer: Therefore, the magnification produced is \( -\frac{1}{2} \), but the magnitude of the magnification is \( 2 \). So, the correct answer is option (1).