In a concave mirror an object is placed at a distance x from the focus, and the image is formed at a distance y from the focus. The focal length of the mirror is

x y

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\frac{x y}{(x - y)}

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\frac{x + y}{2}

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\sqrt{\frac{x}{y}}

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Solution

The correct option is B $\frac{x y}{(x - y)}$
$\begin{matrix} u = - x v = - y f = + f \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \frac{1}{- y} + \frac{1}{x} = \frac{1}{+ f} \frac{x - y}{x y} = \frac{1}{f} \frac{x y}{(x - y)} = f \end{matrix}$

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In a concave mirror an object is placed at a distance x from the focus, and the image is formed at a distance y from the focus. The focal length of the mirror is

The correct option is B xy(x−y)u=−xv=−yf=+f1v−1u=1f1−y+1x=1+fx−yxy=1fxy(x−y)=f

The correct option is B $\frac{x y}{(x - y)}$
$\begin{matrix} u = - x v = - y f = + f \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \frac{1}{- y} + \frac{1}{x} = \frac{1}{+ f} \frac{x - y}{x y} = \frac{1}{f} \frac{x y}{(x - y)} = f \end{matrix}$