1. A concave mirror of focal length 20cm produce an image of magnification-1, what is the distance of object in front of mirror *
Answers
Answer: The mirror formula is [math]\frac {1}{v}+\frac {1}{u}=\frac {1}{f},[/math] where,
[math]\qquad u[/math] is the distance of the object from the mirror,
[math]\qquad v[/math] is the distance of the image from the mirror, and,
[math]\qquad f[/math] is the focal length.
The distance from the mirror to the left is taken as negative and the distance from the mirror to the right is taken as positive.
The magnification is [math]= \frac{h_i}{h_o} = -\frac{v}{u},[/math] where,
[math]\qquad h_i[/math] is the height of the image, and,
[math]\qquad h_o[/math] is the height of the object.
The distance above the principal axis is taken as positive and the distance below the principal axis is taken as negative.
[math]\frac{1}{v}+\frac{1}{u}=\frac{1}{f} \qquad \Rightarrow \qquad \frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{u-f}{uf}.[/math]
[math]\Rightarrow \qquad v = \frac{uf}{u-f}.[/math]
If the magnification is [math]1, \qquad -\frac{v}{u} = 1.[/math]
[math]\Rightarrow \qquad v = -u \qquad \Rightarrow \qquad \frac{uf}{u-f}=-u.[/math]
[math]\Rightarrow \qquad uf=-u^2+uf \qquad \Rightarrow \qquad u=0,[/math]
[math]\qquad[/math] which is not possible.
[math]\Right arrow \qquad[/math] A concave mirror cannot produce an image with magnification [math]1.[/math].