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    Identify the correct relation between radius of curvature ‘R’, object distance ‘u’ and image distance ‘v’ for a spherical mirror.
    Question

    Identify the correct relation between radius of curvature ‘R’, object distance ‘u’ and image distance ‘v’ for a spherical mirror.

    A.

    R=uv/2(u+v)

    B.

    R=2uv/(u+v)

    C.

    R=((u+v))/2uv

    D.

    R=(2(u+v))/uv

    Correct option is B

    Correct Answer: (b) R=2uvu+vR=\frac{2uv}{u+v}

    Explanation:
    For a spherical mirror, the focal length fff is related to the radius of curvature RRR by the formula:

    R=2f

    The mirror formula is:

    1f=1u+1v\frac1f= \frac{1}{u} + \frac{1}{v}​​

    From the mirror formula, the focal length f can be expressed as:

    f=uvu+vf=\frac{uv}{u+v}​​

    Substituting fff into the relation R=2f:

    R=2uvu+vR=2 \frac{uv}{u+v}​​

    Simplifying:

    R=2uvu+vR=\frac{2uv}{u+v}​​

    Thus, the correct relation is R=2uvu+vR= \frac{2uv}{u+v}

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