An object is placed 40 cm from a convex lens with a focal length of 10 cm. Where is the image formed?

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Q: An object is placed 40 cm from a convex lens with a focal length of 10 cm. Where is the image formed?

Solution: Using the lens formula, the image is formed at 30 cm on the opposite side.

Steps: 10

Step 1: Identify the given values. The object distance (u) is -40 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: Use the lens formula: 1/f = 1/v - 1/u, where v is the image distance.
Step 3: Substitute the values into the lens formula: 1/10 = 1/v - 1/(-40).
Step 4: Simplify the equation: 1/10 = 1/v + 1/40.
Step 5: Find a common denominator for the right side, which is 40v: 1/10 = (4 + v)/(40v).
Step 6: Cross-multiply to solve for v: 40v/10 = 4 + v.
Step 7: Simplify the equation: 4v = 4 + v.
Step 8: Rearrange the equation: 4v - v = 4, which gives 3v = 4.
Step 9: Divide both sides by 3 to find v: v = 4/3 cm, which is approximately 1.33 cm.
Step 10: Since the image distance is positive, the image is formed on the opposite side of the lens.