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A beam of light passes through a thin convex lens with a focal length of 15 cm.

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Question: A beam of light passes through a thin convex lens with a focal length of 15 cm. If the object is placed 30 cm from the lens, what is the image distance?

Options:

  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 30 cm

Correct Answer: 20 cm

Solution: 

Using the lens formula, 1/f = 1/v - 1/u; here, f = 15 cm and u = -30 cm. Thus, 1/v = 1/15 + 1/30 = 1/10, giving v = 10 cm.

A beam of light passes through a thin convex lens with a focal length of 15 cm.

Practice Questions

Q1
A beam of light passes through a thin convex lens with a focal length of 15 cm. If the object is placed 30 cm from the lens, what is the image distance?
  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 30 cm

Questions & Step-by-Step Solutions

A beam of light passes through a thin convex lens with a focal length of 15 cm. If the object is placed 30 cm from the lens, what is the image distance?
  • Step 1: Identify the given values. The focal length (f) of the lens is 15 cm, and the object distance (u) is 30 cm.
  • Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -30 cm.
  • Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
  • Step 4: Substitute the known values into the lens formula: 1/15 = 1/v - 1/(-30).
  • Step 5: Simplify the equation: 1/15 = 1/v + 1/30.
  • Step 6: To combine the fractions on the right side, find a common denominator. The common denominator for 15 and 30 is 30.
  • Step 7: Rewrite 1/15 as 2/30. Now the equation looks like: 2/30 = 1/v + 1/30.
  • Step 8: Subtract 1/30 from both sides: 2/30 - 1/30 = 1/v.
  • Step 9: This simplifies to 1/30 = 1/v.
  • Step 10: Invert both sides to find v: v = 30 cm.
  • Lens Formula – The relationship between the focal length (f), object distance (u), and image distance (v) in lens systems, expressed as 1/f = 1/v - 1/u.
  • Sign Convention – Understanding the sign conventions for object distance (u) and image distance (v) in optics, where distances measured against the direction of incident light are negative.
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