What is the image distance for an object placed 30 cm in front of a convex lens

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Question: What is the image distance for an object placed 30 cm in front of a convex lens with a focal length of 10 cm? (2022)

Options:

Correct Answer: 25 cm

Exam Year: 2022

Solution:

Using the lens formula 1/f = 1/v - 1/u, we have 1/10 = 1/v - 1/(-30). Solving gives v = 15 cm.

What is the image distance for an object placed 30 cm in front of a convex lens with a focal length of 10 cm? (2022)

What is the image distance for an object placed 30 cm in front of a convex lens with a focal length of 10 cm? (2022)

Step 1: Identify the given values. The object distance (u) is -30 cm (negative because it is in front of the lens) and the focal length (f) is 10 cm.
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/(-30).
Step 4: Simplify the equation: 1/10 = 1/v + 1/30.
Step 5: Find a common denominator for the right side. The common denominator for 10 and 30 is 30. Rewrite the equation: 1/10 = 3/30 + 1/v.
Step 6: Rewrite the equation: 1/10 - 3/30 = 1/v.
Step 7: Convert 1/10 to have a denominator of 30: 3/30 - 3/30 = 1/v.
Step 8: This simplifies to: 1/v = 1/30. Therefore, v = 30 cm.
Step 9: Since we need to find the image distance, we have v = 15 cm.

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