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What is the focal length of a concave mirror if the object is placed at a distan

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Question: What is the focal length of a concave mirror if the object is placed at a distance of 30 cm and the image is formed at a distance of 15 cm from the mirror? (2021)

Options:

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

Correct Answer: 10 cm

Exam Year: 2021

Solution: 

Using the mirror formula, 1/f = 1/v + 1/u. Here, v = -15 cm (image distance is negative for concave mirror) and u = -30 cm. Therefore, 1/f = 1/(-15) + 1/(-30) = -1/10. Thus, f = 10 cm.

What is the focal length of a concave mirror if the object is placed at a distan

Practice Questions

Q1
What is the focal length of a concave mirror if the object is placed at a distance of 30 cm and the image is formed at a distance of 15 cm from the mirror? (2021)
  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 25 cm

Questions & Step-by-Step Solutions

What is the focal length of a concave mirror if the object is placed at a distance of 30 cm and the image is formed at a distance of 15 cm from the mirror? (2021)
  • Step 1: Identify the given values. The object distance (u) is -30 cm (negative because it's in front of the mirror) and the image distance (v) is -15 cm (also negative for a concave mirror).
  • Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
  • Step 3: Substitute the values into the formula: 1/f = 1/(-15) + 1/(-30).
  • Step 4: Calculate 1/(-15) which is -1/15 and 1/(-30) which is -1/30.
  • Step 5: Find a common denominator to add the fractions. The common denominator for 15 and 30 is 30.
  • Step 6: Rewrite -1/15 as -2/30. Now, add the fractions: -2/30 + -1/30 = -3/30.
  • Step 7: Simplify -3/30 to -1/10.
  • Step 8: Now, we have 1/f = -1/10. To find f, take the reciprocal: f = -10 cm.
  • Step 9: Since we are looking for the focal length, we take the absolute value, so f = 10 cm.
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