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A convex lens has a focal length of 20 cm. If an object is placed at a distance

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Question: A convex lens has a focal length of 20 cm. If an object is placed at a distance of 40 cm from the lens, what is the distance of the image from the lens?

Options:

  1. 20 cm
  2. 40 cm
  3. 60 cm
  4. 80 cm

Correct Answer: 20 cm

Solution: 

Using the lens formula 1/f = 1/v - 1/u, where f = 20 cm and u = -40 cm, we find v = 20 cm. The image is formed at 20 cm on the opposite side.

A convex lens has a focal length of 20 cm. If an object is placed at a distance

Practice Questions

Q1
A convex lens has a focal length of 20 cm. If an object is placed at a distance of 40 cm from the lens, what is the distance of the image from the lens?
  1. 20 cm
  2. 40 cm
  3. 60 cm
  4. 80 cm

Questions & Step-by-Step Solutions

A convex lens has a focal length of 20 cm. If an object is placed at a distance of 40 cm from the lens, what is the distance of the image from the lens?
  • Step 1: Identify the given values. The focal length (f) of the lens is 20 cm, and the object distance (u) is 40 cm.
  • Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -40 cm.
  • Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
  • Step 4: Substitute the known values into the lens formula: 1/20 = 1/v - 1/(-40).
  • Step 5: Simplify the equation: 1/20 = 1/v + 1/40.
  • Step 6: Find a common denominator for the right side. The common denominator for 20 and 40 is 40.
  • Step 7: Rewrite the equation: 1/20 = 2/40 + 1/v.
  • Step 8: Now, rewrite 1/20 as 2/40: 2/40 = 2/40 + 1/v.
  • Step 9: Subtract 2/40 from both sides: 0 = 1/v - 2/40.
  • Step 10: Rearranging gives us 1/v = 2/40, which simplifies to 1/v = 1/20.
  • Step 11: Take the reciprocal to find v: v = 20 cm.
  • Step 12: The image is formed at a distance of 20 cm on the opposite side of the lens.
  • Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) of a lens, expressed as 1/f = 1/v - 1/u.
  • Sign Convention – Understanding the sign convention for distances in optics, where object distance (u) is negative for real objects placed in front of the lens.
  • Image Formation – Determining the position and nature of the image formed by a convex lens based on the object distance and focal length.
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