An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. Where is the image formed?

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Q: An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. Where is the image formed?

Solution: Using the lens formula, 1/f = 1/v - 1/u, we find v = 30 cm, meaning the image is formed 30 cm on the opposite side.

Steps: 9

Step 1: Identify the given values. The object distance (u) is -15 cm (negative because it is on the same side as the object) and the focal length (f) is +10 cm (positive for a convex lens).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/10 = 1/v - 1/(-15).
Step 4: Simplify the equation: 1/10 = 1/v + 1/15.
Step 5: Find a common denominator for the right side, which is 30. Rewrite the equation: 1/10 = 1/v + 2/30.
Step 6: Convert 1/10 to have a denominator of 30: 3/30 = 1/v + 2/30.
Step 7: Rearrange the equation: 3/30 - 2/30 = 1/v, which simplifies to 1/30 = 1/v.
Step 8: Take the reciprocal to find v: v = 30 cm.
Step 9: Interpret the result: The image is formed 30 cm on the opposite side of the lens.