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(A) For a spherical mirror,Newton's formula relates the distances of the object and image from the focus $F$. Let $x_{1}$ and $x_{2}$ be the distances

Vedclass · Accepted Answer

$\frac{2 d_{1} d_{2}}{d_{1}-d_{2}}$

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(A) For a spherical mirror,Newton's formula relates the distances of the object and image from the focus $F$. Let $x_{1}$ and $x_{2}$ be the distances of the object and image from the focus,respectively. The formula is $x_{1} x_{2} = f^{2}$.In this problem,the distances are measured from the centre of curvature $C$. The distance of the focus $F$ from $C$ is the focal length $f$. Thus,the distance of the object from the focus is $x_{1} = d_{1} + f$,and the distance of the image from the focus is $x_{2} = f - d_{2}$.Substituting these into Newton's formula: $(f + d_{1})(f - d_{2}) = f^{2}$.Expanding the equation: $f^{2} - f d_{2} + f d_{1} - d_{1} d_{2} = f^{2}$.Simplifying: $f(d_{1} - d_{2}) = d_{1} d_{2}$.Therefore,the focal length is $f = \frac{d_{1} d_{2}}{d_{1} - d_{2}}$.The radius of curvature $R$ is given by $R = 2f$.Hence,$R = \frac{2 d_{1} d_{2}}{d_{1} - d_{2}}$.

An object is placed beyond the centre of curvature $C$ of a concave mirror. If the distance of the object is $d_{1}$ from $C$ and the distance of the image formed is $d_{2}$ from $C$,the radius of curvature of this mirror is

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