A person wants a real image of his own, 3 times enlarged. Where should he stand
in front of a concave mirror of radius of curvature 30cm?
Answers
Ａｎｓｗｅｒ:
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cm
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−x
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−xMagnification of image m = 3m=3
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−xMagnification of image m = 3m=3\therefore∴ m = \dfrac{-v}{u}m=u−v
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−xMagnification of image m = 3m=3\therefore∴ m = \dfrac{-v}{u}m=u−vOr 3 = \dfrac{-v}{-x}3=−x−v \implies v =3x⟹v =3x
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−xMagnification of image m = 3m=3\therefore∴ m = \dfrac{-v}{u}m=u−vOr 3 = \dfrac{-v}{-x}3=−x−v \implies v =3x⟹v =3xUsing mirror formula : \dfrac{1}{v}+\dfrac{1}{u} = \dfrac{1}{f}v1+u1=f1
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−xMagnification of image m = 3m=3\therefore∴ m = \dfrac{-v}{u}m=u−vOr 3 = \dfrac{-v}{-x}3=−x−v \implies v =3x⟹v =3xUsing mirror formula : \dfrac{1}{v}+\dfrac{1}{u} = \dfrac{1}{f}v1+u1=f1\therefore∴ \dfrac{1}{3x}+\dfrac{1}{-x} = \dfrac{1}{-15}3x1+−x1=−151 \implies x = 10⟹x=10 cm
Focal length of concave mirror f = \dfrac{-R}{2} = \dfrac{-30}{2} =-15f=2−R=2−30=−15 cmLet the person stands at a distance xx infront of mirror i.e. u = -xu=−xMagnification of image m = 3m=3\therefore∴ m = \dfrac{-v}{u}m=u−vOr 3 = \dfrac{-v}{-x}3=−x−v \implies v =3x⟹v =3xUsing mirror formula : \dfrac{1}{v}+\dfrac{1}{u} = \dfrac{1}{f}v1+u1=f1\therefore∴ \dfrac{1}{3x}+\dfrac{1}{-x} = \dfrac{1}{-15}3x1+−x1=−151 \implies x = 10⟹x=10 cmThus the person should stand at a distance of 1010 cm infront of the mirror.