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If a lens forms a real image at a distance of 40 cm from the lens, and the objec

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Question: If a lens forms a real image at a distance of 40 cm from the lens, and the object is placed at 60 cm, what is the focal length of the lens?

Options:

  1. 15 cm
  2. 20 cm
  3. 25 cm
  4. 30 cm

Correct Answer: 25 cm

Solution: 

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/40 - 1/(-60) = 1/40 + 1/60 = 1/24. Therefore, f = 24 cm.

If a lens forms a real image at a distance of 40 cm from the lens, and the objec

Practice Questions

Q1
If a lens forms a real image at a distance of 40 cm from the lens, and the object is placed at 60 cm, what is the focal length of the lens?
  1. 15 cm
  2. 20 cm
  3. 25 cm
  4. 30 cm

Questions & Step-by-Step Solutions

If a lens forms a real image at a distance of 40 cm from the lens, and the object is placed at 60 cm, what is the focal length of the lens?
  • Step 1: Identify the given values. The image distance (v) is 40 cm and the object distance (u) is -60 cm (negative because the object is on the same side as the incoming light).
  • Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
  • Step 3: Substitute the values into the lens formula: 1/f = 1/40 - 1/(-60).
  • Step 4: Simplify the equation: 1/f = 1/40 + 1/60.
  • Step 5: Find a common denominator to add the fractions. The common denominator of 40 and 60 is 120.
  • Step 6: Convert the fractions: 1/40 = 3/120 and 1/60 = 2/120.
  • Step 7: Add the fractions: 1/f = 3/120 + 2/120 = 5/120.
  • Step 8: Simplify the fraction: 1/f = 1/24.
  • Step 9: Take the reciprocal to find the focal length: f = 24 cm.
  • Lens Formula – The lens formula relates the focal length (f), the image distance (v), and the object distance (u) through the equation 1/f = 1/v - 1/u.
  • Sign Convention – Understanding the sign convention for distances is crucial; object distance (u) is negative for real objects placed on the same side as the incoming light.
  • Real and Virtual Images – Recognizing the difference between real and virtual images, where real images are formed on the opposite side of the lens from the object.
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