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MCQEasyJEE 2025Reflection & Spherical Mirrors

JEE Physics 2025 Question with Solution

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm12 \, \text{cm}, at same distance of 18 cm18 \, \text{cm} from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

  • A

    12\frac{1}{2}

  • B

    22

  • C

    33

  • D

    13\frac{1}{3}

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Both mirrors have radius of curvature R=12 cmR = 12 \, \text{cm} and the object is placed at distance 18 cm18 \, \text{cm} from each mirror.

Find: The ratio of image sizes formed by the convex mirror and the concave mirror.

Using the magnification formula for mirrors:

m=fu−fm = \frac{f}{u-f}

For the concave mirror, the object distance is u=−18 cmu = -18 \, \text{cm}), and the focal length is

f=R2=6 cmf = \frac{R}{2} = 6 \, \text{cm}

where R=12 cmR = 12 \, \text{cm}. Then

m1=618−6=12m_1 = \frac{6}{18 - 6} = \frac{1}{2}
Mirror diagram showing an object O placed 18 cm from a spherical mirror with radius of curvature 12 cm, with principal axis and distance arrow marked.

For the convex mirror, the object distance is the same, and the focal length is positive:

m2=618+6=14m_2 = \frac{6}{18 + 6} = \frac{1}{4}

Hence, the ratio of the sizes of the images formed by the convex mirror and the concave mirror is

m2m1=1/41/2=12\frac{m_2}{m_1} = \frac{1/4}{1/2} = \frac{1}{2}
Second mirror diagram showing an object O at 18 cm from a spherical mirror with radius of curvature 12 cm, principal axis drawn and distance indicated by arrows.

Therefore, the ratio of image sizes is 12\frac{1}{2}. The correct option is A.

Magnification Comparison

Given: Same object distance and same radius of curvature for both mirrors.

Find: Compare the magnitudes of magnifications for convex and concave mirrors.

First compute the focal length from

f=R2=122=6 cmf = \frac{R}{2} = \frac{12}{2} = 6 \, \text{cm}

From the extracted working, the magnifications are

mconcave=12,mconvex=14m_{\text{concave}} = \frac{1}{2}, \qquad m_{\text{convex}} = \frac{1}{4}

So the required ratio is

mconvexmconcave=1/41/2=12\frac{m_{\text{convex}}}{m_{\text{concave}}} = \frac{1/4}{1/2} = \frac{1}{2}

Thus, the image formed by the convex mirror is half the size of the image formed by the concave mirror.

Common mistakes

  • Using R=12 cmR = 12 \, \text{cm} directly as the focal length is incorrect because for a spherical mirror f=R2f = \frac{R}{2}. Always convert radius of curvature to focal length first.

  • Comparing image distances instead of magnifications is wrong because the question asks for the sizes of images. Use the magnification relation and then take the ratio mconvexmconcave\frac{m_{\text{convex}}}{m_{\text{concave}}}.

  • Reversing the required ratio leads to the answer 22, which is incorrect here. The question asks for convex mirror image size : concave mirror image size, so keep that order while dividing.

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