What is the focal length of a lens if it forms a virtual image at a distance of

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

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

Step 1: Understand the lens formula, which is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Step 2: Identify the values given in the problem. 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 3: Substitute the values into the lens formula: 1/f = 1/v - 1/u becomes 1/f = 1/12 - 1/(-8).
Step 4: Calculate 1/12 - (-1/8). This is the same as 1/12 + 1/8.
Step 5: Find a common denominator for 12 and 8, which is 24. Rewrite the fractions: 1/12 = 2/24 and 1/8 = 3/24.
Step 6: Add the fractions: 2/24 + 3/24 = 5/24.
Step 7: Now, we have 1/f = 5/24. To find f, take the reciprocal: f = 24/5.
Step 8: Calculate 24/5, which equals 4.8 cm. Since the image is virtual, the focal length is negative: f = -4.8 cm.

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