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A lens forms a real image at a distance of 40 cm from the lens when the object i

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Question: A lens forms a real image at a distance of 40 cm from the lens when the object is placed at 20 cm. What is the focal length of the lens?

Options:

  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 25 cm

Correct Answer: 10 cm

Solution: 

Using the lens formula, 1/f = 1/v - 1/u. Here, v = 40 cm, u = -20 cm. Solving gives f = 10 cm.

A lens forms a real image at a distance of 40 cm from the lens when the object i

Practice Questions

Q1
A lens forms a real image at a distance of 40 cm from the lens when the object is placed at 20 cm. What is the focal length of the lens?
  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 25 cm

Questions & Step-by-Step Solutions

A lens forms a real image at a distance of 40 cm from the lens when the object is placed at 20 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 20 cm.
  • Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -20 cm.
  • Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
  • Step 4: Substitute the values into the formula: 1/f = 1/40 - 1/(-20).
  • Step 5: Calculate 1/40, which is 0.025, and 1/(-20), which is -0.05.
  • Step 6: Now, calculate 1/f = 0.025 + 0.05.
  • Step 7: Add the two values: 1/f = 0.025 + 0.05 = 0.075.
  • Step 8: To find f, take the reciprocal: f = 1/0.075.
  • Step 9: Calculate f, which gives you f = 13.33 cm (approximately).
  • 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 lenses is crucial, where 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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