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A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front

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Question: A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front of the mirror. Where will the image be formed?

Options:

  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 30 cm

Correct Answer: 20 cm

Solution: 

Using the mirror formula, 1/f = 1/v + 1/u, where f = -10 cm (concave mirror), u = -30 cm. Solving gives v = -15 cm, which means the image is formed 15 cm in front of the mirror.

A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front

Practice Questions

Q1
A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front of the mirror. Where will the image be formed?
  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 30 cm

Questions & Step-by-Step Solutions

A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front of the mirror. Where will the image be formed?
  • Step 1: Identify the given values. The focal length (f) of the concave mirror is 10 cm, but since it's a concave mirror, we use -10 cm. The object distance (u) is 30 cm, and we use -30 cm because we follow the sign convention.
  • Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
  • Step 3: Substitute the values into the formula: 1/(-10) = 1/v + 1/(-30).
  • Step 4: Simplify the equation: -1/10 = 1/v - 1/30.
  • Step 5: Find a common denominator for the right side. The common denominator for 10 and 30 is 30. Rewrite the equation: -1/10 = 3/(30v) - 1/(30).
  • Step 6: Combine the fractions on the right side: -1/10 = (3 - 1)/(30v) = 2/(30v).
  • Step 7: Cross-multiply to solve for v: -1 * 30v = 2 * 10, which gives -30v = 20.
  • Step 8: Divide both sides by -30 to find v: v = -20/30 = -2/3 cm, which simplifies to v = -15 cm.
  • Step 9: Interpret the result. The negative sign indicates that the image is formed in front of the mirror, 15 cm away.
  • Mirror Formula – The relationship between the focal length (f), object distance (u), and image distance (v) in mirror optics, expressed as 1/f = 1/v + 1/u.
  • Sign Convention – Understanding the sign conventions for concave mirrors, where focal length is negative and object distance is negative when measured in the direction of the incoming light.
  • Image Formation – Determining the characteristics of the image formed by a concave mirror, including its position, nature (real or virtual), and orientation.
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