An object is placed at 20 cm in front of a concave mirror and the image formed by this mirror is at 60 cm in front of the concave mirror. What is the focal length of the mirror?

  1. -15 cm
  2. -20 cm
  3. -30 cm
  4. None of the above

Answer (Detailed Solution Below)

Option 1 : -15 cm
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Detailed Solution

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CONCEPT:

  • Concave mirror: The mirror in which the rays converge after falling on it is known as the concave mirror.
    • Concave mirrors are also known as a converging mirror.
    • The focal length of a concave mirror is negative according to the sign convention.
  • Mirror Formula: The following formula is known as the mirror formula:

\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

where f is focal length v is the distance of the image from the mirror, and u is the distance of the object from the mirror.

CALCULATION:

Given that u = -20 cm and v = -60 cm

Mirror formula \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

\(\frac{1}{f}=\frac{1}{-20}+\frac{1}{-60}\)

f = -60/4= -15 cm

So the correct answer is option 1.

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