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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 60 cm from the lens, what is the distance of the image from the lens?

Options:

  1. 15 cm
  2. 30 cm
  3. 45 cm
  4. 60 cm

Correct Answer: 45 cm

Solution: 

Using the lens formula 1/f = 1/v - 1/u, we find v = 30 cm.

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 60 cm from the lens, what is the distance of the image from the lens?
  1. 15 cm
  2. 30 cm
  3. 45 cm
  4. 60 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 60 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 -60 cm (we use a negative sign for object distance in lens formula).
  • Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
  • Step 3: Substitute the known values into the lens formula: 1/20 = 1/v - 1/(-60).
  • Step 4: Simplify the equation: 1/20 = 1/v + 1/60.
  • Step 5: Find a common denominator for the right side of the equation. The common denominator for 20 and 60 is 60. Rewrite the equation: 1/20 = 3/60 + 1/v.
  • Step 6: Rewrite 1/20 as 3/60 - 1/v: 3/60 - 1/v = 1/20.
  • Step 7: Rearrange the equation to isolate 1/v: 1/v = 3/60 - 1/20.
  • Step 8: Convert 1/20 to have a denominator of 60: 1/20 = 3/60. Now the equation is: 1/v = 3/60 - 3/60.
  • Step 9: Calculate 1/v: 1/v = 0.05 - 0.05 = 0. This means v = 30 cm.
  • Step 10: The distance of the image from the lens is 30 cm.
  • Lens Formula – The lens formula relates the focal length (f), the object distance (u), and the image distance (v) in a lens system, expressed as 1/f = 1/v - 1/u.
  • Convex Lens Properties – A convex lens converges light rays and can produce real and virtual images depending on the position of the object relative to the focal length.
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