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 15 cm when the object is placed at 10 cm?

What is the focal length of a lens if it forms a virtual image at a distance of 15 cm when the object is placed at 10 cm?

Step 1: Identify the given values. The object distance (u) is -10 cm (negative because it's on the same side as the object) and the image distance (v) is -15 cm (negative because it's 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/(-15) - 1/(-10).
Step 4: Calculate 1/(-15) which is -1/15 and 1/(-10) which is -1/10.
Step 5: Combine the fractions: 1/f = -1/15 + 1/10.
Step 6: Find a common denominator for the fractions. The common denominator for 15 and 10 is 30.
Step 7: Rewrite the fractions: -1/15 = -2/30 and 1/10 = 3/30.
Step 8: Add the fractions: 1/f = -2/30 + 3/30 = 1/30.
Step 9: Take the reciprocal to find f: f = 30 cm.
Step 10: Since the focal length is negative for a virtual image, the final answer is f = -30 cm.

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