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A concave mirror produces a virtual image of an object placed 10 cm in front of

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Question: A concave mirror produces a virtual image of an object placed 10 cm in front of it. If the focal length of the mirror is 5 cm, what is the distance of the image from the mirror?

Options:

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

Correct Answer: 10 cm

Solution: 

Using the mirror formula, 1/f = 1/v + 1/u. Here, f = -5 cm (concave mirror), u = -10 cm. Solving gives v = -10 cm.

A concave mirror produces a virtual image of an object placed 10 cm in front of

Practice Questions

Q1
A concave mirror produces a virtual image of an object placed 10 cm in front of it. If the focal length of the mirror is 5 cm, what is the distance of the image from the mirror?
  1. 5 cm
  2. 10 cm
  3. 15 cm
  4. 20 cm

Questions & Step-by-Step Solutions

A concave mirror produces a virtual image of an object placed 10 cm in front of it. If the focal length of the mirror is 5 cm, what is the distance of the image from the mirror?
  • Step 1: Identify the given values. The focal length (f) of the concave mirror is 5 cm, but since it's a concave mirror, we use -5 cm. The object distance (u) is 10 cm in front of the mirror, so we use -10 cm.
  • Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
  • Step 3: Substitute the values into the formula: 1/(-5) = 1/v + 1/(-10).
  • Step 4: Simplify the equation: -1/5 = 1/v - 1/10.
  • Step 5: To combine the fractions, find a common denominator. The common denominator for 5 and 10 is 10.
  • Step 6: Rewrite -1/5 as -2/10: -2/10 = 1/v - 1/10.
  • Step 7: Add 1/10 to both sides: -2/10 + 1/10 = 1/v.
  • Step 8: Simplify the left side: -1/10 = 1/v.
  • Step 9: Take the reciprocal of both sides to find v: v = -10 cm.
  • Step 10: Interpret the result: The negative sign indicates that the image is virtual and located 10 cm behind the mirror.
  • Mirror Formula – The relationship between the focal length (f), object distance (u), and image distance (v) in mirror optics, given by 1/f = 1/v + 1/u.
  • Sign Convention – Understanding the sign conventions for distances in optics, where distances measured in the direction of the incoming light are negative.
  • Virtual Images – Characteristics of virtual images produced by concave mirrors, which are formed on the same side as the object and cannot be projected onto a screen.
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