A) \[\left( \frac{f}{u-f} \right)\,b\]
B) \[{{\left( \frac{f}{u-f} \right)}^{2}}\,b\]
C) \[\left( \frac{f}{u-f} \right)\,{{b}^{2}}\]
D) \[\left( \frac{f}{u-f} \right)\,\]
Correct Answer: B
Solution :
The focal length of a concave mirror is \[\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\] ?(1) Where v and u are the image distance and object distance respectively. Differentiating Eq. (1), we get \[0=\frac{1}{{{v}^{2}}}dv-\frac{1}{{{u}^{2}}}du\] \[\Rightarrow \] \[du=-\frac{{{v}^{2}}}{{{u}^{2}}}b\] ?(2) \[\left( du=b \right)\] Also \[\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{u-f}{fu}\] \[\Rightarrow \] \[\frac{u}{v}=\frac{u-f}{f}\] \[\Rightarrow \] \[\frac{v}{u}=\frac{f}{u-f}\] ?(3) From Eq. (2) and (3), we get \[du=-{{\left( \frac{f}{u-f} \right)}^{2}}b\] Hence, size of image\[={{\left( \frac{f}{u-f} \right)}^{2}}b\]
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