Question

An object is placed in front of a convex lens of focal length 12 cm. If the size of the real image formed is half the size of the object, then the distance of the object from the lens is:

• A. 48 cm
• B. 36 cm
• C. 26 cm
• D. 30 cm

Hint:

Use the magnification formula along with the lens equation to find the object distance when the image size is related to the object size.

Answer 1

The Correct Option is B

For a convex lens, the magnification \( M \) is given by the formula: \[ M = \frac{\text{image height}}{\text{object height}} = \frac{v}{u} \] Where: - \( M = \frac{1}{2} \) (the image size is half the object size) - \( u \) is the object distance, and \( v \) is the image distance. Also, for a lens, the lens equation is: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where \( f = 12 \, \text{cm} \) (focal length of the lens). Using the magnification equation: \[ \frac{1}{2} = \frac{v}{u} \] This gives: \[ v = \frac{u}{2} \] Substitute into the lens equation: \[ \frac{1}{12} = \frac{2}{u} - \frac{1}{u} \] Solving for \( u \): \[ \frac{1}{12} = \frac{1}{u} \] \[ u = 36 \, \text{cm} \] Thus, the object distance is 36 cm.