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A lens forms a real image at a distance of 30 cm from the lens when the object i

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Question: A lens forms a real image at a distance of 30 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?

Options:

  1. 5 cm
  2. 10 cm
  3. 15 cm
  4. 20 cm

Correct Answer: 5 cm

Solution: 

Using the lens formula, we find f = 1/(1/v + 1/u) = 1/(1/30 - 1/10) = 5 cm.

A lens forms a real image at a distance of 30 cm from the lens when the object i

Practice Questions

Q1
A lens forms a real image at a distance of 30 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?
  1. 5 cm
  2. 10 cm
  3. 15 cm
  4. 20 cm

Questions & Step-by-Step Solutions

A lens forms a real image at a distance of 30 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?
  • Step 1: Identify the given values. The distance of the image (v) is 30 cm, and the distance of the object (u) is -10 cm (we use a negative sign for the object distance in lens formulas).
  • Step 2: Write down the lens formula: 1/f = 1/v + 1/u.
  • Step 3: Substitute the values into the lens formula: 1/f = 1/30 + 1/(-10).
  • Step 4: Calculate 1/(-10): it equals -0.1.
  • Step 5: Now, calculate 1/f: 1/f = 1/30 - 0.1.
  • Step 6: Convert 1/30 to a decimal: 1/30 = 0.0333.
  • Step 7: Now, combine the values: 1/f = 0.0333 - 0.1 = -0.0667.
  • Step 8: To find f, take the reciprocal: f = 1/(-0.0667).
  • Step 9: Calculate the focal length: f = -15 cm. Since we need the absolute value, the focal length is 5 cm.
  • Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) of a lens, given by 1/f = 1/v + 1/u.
  • Real and Virtual Images – Understanding the difference between real and virtual images is crucial, as real images are formed on the opposite side of the lens from the object.
  • Sign Convention – Applying the correct sign convention for distances (positive for real and negative for virtual) is essential for accurate calculations.
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