Question:medium

A convex lens has a focal length of 20 cm. An object is placed 30 cm in front of the lens. What is the image distance from the lens?

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In lens problems, follow the sign convention carefully: object distance \( u \) is negative for real objects, and focal length \( f \) is positive for convex lenses. A positive image distance \( v \) indicates a real image.
Updated On: Nov 26, 2025
  • \( 12 \, \text{cm} \)
  • \( 60 \, \text{cm} \)
  • \( 15 \, \text{cm} \)
  • \( 30 \, \text{cm} \)
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The Correct Option is B

Solution and Explanation

To determine the image distance for a convex lens, the lens formula is applied: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Parameters are defined as: - \( f = 20 \, \text{cm} \) (focal length, positive for a convex lens) - \( u = -30 \, \text{cm} \) (object distance, negative as the object is on the incident light's side) - \( v \) represents the image distance to be calculated. The lens formula is rearranged to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \] Substituting the known values yields: \[ \frac{1}{v} = \frac{1}{20} + \frac{1}{-30} \] This simplifies to: \[ \frac{1}{v} = \frac{1}{20} - \frac{1}{30} \] Using a common denominator (60), the equation becomes: \[ \frac{1}{v} = \frac{3}{60} - \frac{2}{60} = \frac{3 - 2}{60} = \frac{1}{60} \] Therefore, the image distance is: \[ v = 60 \, \text{cm} \] The positive value of \( v \) signifies that the image is formed on the side of the lens opposite to the object, consistent with a real image formed by a convex lens when the object is beyond the focal point. Consequently, the image distance from the lens is \( 60 \, \text{cm} \).
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