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MCQMediumJEE 2025Reflection & Spherical Mirrors

JEE Physics 2025 Question with Solution

A finite size object is placed normal to the principal axis at a distance of 30 cm30 \, \text{cm} from a convex mirror of focal length 30 cm30 \, \text{cm}. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

  • A

    45 cm45 \, \text{cm}

  • B

    7.5 cm7.5 \, \text{cm}

  • C

    22.5 cm22.5 \, \text{cm}

  • D

    15 cm15 \, \text{cm}

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Object distance from the convex mirror is u=−30 cmu = -30 \, \text{cm} and focal length of the convex mirror is f=30 cmf = 30 \, \text{cm}.

Find: The distance between the convex mirror and the plane mirror.

For the convex mirror, use the mirror formula:

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

Substituting the given values:

130=1v−130\frac{1}{30} = \frac{1}{v} - \frac{1}{30} 1v=130+130=230\frac{1}{v} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} v=15 cmv = 15 \, \text{cm}

So, the convex mirror forms a virtual image 15 cm15 \, \text{cm} behind the mirror.

Let the distance between the two mirrors be DD. For a plane mirror, the image is formed at the same distance behind the mirror as the object is in front of it. For the images formed by the convex mirror and the plane mirror to coincide, the image point must lie midway between the convex mirror image position and the plane mirror.

Thus,

D+D=15 cmD + D = 15 \, \text{cm} 2D=15 cm2D = 15 \, \text{cm} D=7.5 cmD = 7.5 \, \text{cm}

Therefore, the distance between the two mirrors is 7.5 cm7.5 \, \text{cm}. The correct option is B.

Image Coincidence Idea

Given: The convex mirror forms a virtual image for an object placed 30 cm30 \, \text{cm} in front of it, and its focal length is 30 cm30 \, \text{cm}.

Find: The separation between the convex mirror and the plane mirror.

From the mirror formula, the convex mirror image is obtained at 15 cm15 \, \text{cm} behind the convex mirror.

For coincidence, the plane mirror must form its image at exactly the same point. A plane mirror places the image as far behind itself as the object is in front of it, so the coinciding point must be at equal distances from the plane mirror on both sides.

Hence the mirror separation is half of 15 cm15 \, \text{cm}:

D=152=7.5 cmD = \frac{15}{2} = 7.5 \, \text{cm}

Therefore, the correct option is B.

Common mistakes

  • Using the wrong sign convention for the convex mirror. Taking u=+30 cmu = +30 \, \text{cm} for a real object gives an incorrect image position. Use u=−30 cmu = -30 \, \text{cm} and f=+30 cmf = +30 \, \text{cm} with the mirror formula.

  • Assuming the plane mirror should be placed 15 cm15 \, \text{cm} away because the convex mirror image is 15 cm15 \, \text{cm} behind it. This is wrong because the plane mirror image forms symmetrically about the plane mirror. The mirror must be placed so that the coinciding image point is equally split, giving half the distance.

  • Confusing the image formed by the convex mirror with a real image. The convex mirror produces a virtual image behind the mirror, and that virtual position is the point that must coincide with the plane mirror image.

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