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

What is the focal length of a convex lens if it forms a real image at a distance of 30 cm when the object is placed at 15 cm from the lens?

What is the focal length of a convex lens if it forms a real image at a distance of 30 cm when the object is placed at 15 cm from the lens?

Correct Answer: 20 cm

Step 1: Identify the given values. The distance of the image (v) is 30 cm, and the distance of the object (u) is 15 cm. Since the object is on the same side as the incoming light, we use u = -15 cm.
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the values into the lens formula. We have v = 30 cm and u = -15 cm, so the equation becomes 1/f = 1/30 - 1/(-15).
Step 4: Calculate 1/30. This equals approximately 0.0333.
Step 5: Calculate 1/(-15). This equals approximately -0.0667.
Step 6: Now, add the two results: 1/f = 0.0333 + 0.0667 = 0.1.
Step 7: To find f, take the reciprocal of 0.1. So, f = 1/0.1 = 10 cm.

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