Concave mirror
A) -5 cm
B) +5 cm
C) +7.5 cm
D) -7.5 cm
Correct Answer: A
Solution :
Key Idea: Magnification is ratio of size of image to that of object. Here, \[u=-1.5\,\,f,\,f=-f\] From concave mirror formula, \[\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\] we have, \[\frac{1}{(-f)}=\frac{1}{v}+\frac{1}{(-1.5f)}\] \[\therefore \] \[\frac{1}{v}=-\frac{1}{v}+\frac{1}{(-1.5f)}\] \[\therefore \] \[\frac{1}{v}=-\frac{1}{3f}\] Or \[v=-3\,f\] Now, magnification in mirror is given by \[m=\frac{I}{O}=\frac{v}{-u}\] where \[I\] is size of image, and O is size of object. Here, \[0=+2.5\,\,cm\] \[\therefore \] \[\frac{I}{2.5}=\frac{-3f}{-(-1.5f)}\] \[\therefore \] \[I=-5\,cm\] Note: In case of a concave mirror, magnification may be positive or negative, but in case of convex mirror magnification is positive only.
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