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What is the focal length of a concave mirror if the object distance is 30 cm and

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Question: What is the focal length of a concave mirror if the object distance is 30 cm and the image distance is 15 cm? (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 (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = -10 cm.

What is the focal length of a concave mirror if the object distance is 30 cm and

Practice Questions

Q1
What is the focal length of a concave mirror if the object distance is 30 cm and the image distance is 15 cm? (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 distance is 30 cm and the image distance is 15 cm? (2021)
  • Step 1: Identify the mirror formula, which is 1/f = 1/v + 1/u.
  • Step 2: Understand the variables: f is the focal length, v is the image distance, and u is the object distance.
  • Step 3: Note that for a concave mirror, the image distance (v) is negative for real images. Here, v = -15 cm.
  • Step 4: The object distance (u) is also negative for mirrors. Here, u = -30 cm.
  • Step 5: Substitute the values into the mirror formula: 1/f = 1/(-15) + 1/(-30).
  • Step 6: Calculate 1/(-15) + 1/(-30). First, find a common denominator, which is 30. So, 1/(-15) = -2/30 and 1/(-30) = -1/30.
  • Step 7: Add the fractions: -2/30 + -1/30 = -3/30.
  • Step 8: Simplify -3/30 to -1/10. So, 1/f = -1/10.
  • Step 9: To find f, take the reciprocal of -1/10, which gives f = -10 cm.
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