A lens forms a virtual image at a distance of 12 cm when the object is placed at

A lens forms a virtual image at a distance of 12 cm when the object is placed at 8 cm. What is the focal length of the lens?

A lens forms a virtual image at a distance of 12 cm when the object is placed at 8 cm. What is the focal length of the lens?

Step 1: Identify the given values. The object distance (u) is -8 cm (negative because it is on the same side as the object) and the image distance (v) is 12 cm (positive because it is a virtual image).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the values into the lens formula: 1/f = 1/12 - 1/(-8).
Step 4: Calculate 1/12, which is 0.0833, and 1/(-8), which is -0.125. So, 1/f = 0.0833 + 0.125.
Step 5: Add the two fractions: 1/f = 0.0833 + 0.125 = 0.2083.
Step 6: To find f, take the reciprocal of 0.2083: f = 1/0.2083.
Step 7: Calculate f, which is approximately 4 cm.

Lens Formula – The lens formula relates the focal length (f), the object distance (u), and the image distance (v) using the equation 1/f = 1/v - 1/u.
Virtual Image Formation – A virtual image is formed when the light rays diverge, and it appears on the same side of the lens as the object.