Question

if magnification of convex mirror is 1/2 when object placed at certain distance.
where should object be placed to get magnification
1/3

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Answer 1

If magnification of convex mirror is 1/2 when object placed at certain distance.

where should object be placed to get magnification of 1/3?

Good question,

Here is your perfect answer!

Let the first case distance of object from mirror be u and image be v.

m = - v/u

=) 1/2 = - v/u

=) u = - 2v,

1/f = 1/u + 1/v

=) 1/f = 1/-2v + 1/v

=) 1/f = 1/2v

=) f = 2v

I think your question has some fault, so I put image distance same.

=) - v/u' = 1/3

(second case)

=) u' = - 3v

This is your answer!

Answer 2

$\huge \bf{ \red{ANSWER}}$

$\bf{QUESTION}$
if magnification of convex mirror is 1/2 when object placed at certain distance.
where should object be placed to get magnification
1/3


$\bf{step \: by \: step \: explanation}$
first case


$\bf{\frac{mi}{mu} = \frac{ - v}{u}}$
$\bf{ \frac{1}{2} = \frac{ - v}{u} }$



u=-2v

$\bf{ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}}$

$\bf{ \frac{1}{f} = \frac{1}{v} + \frac{1}{ - 2v}}$

$\bf{ \frac{1}{f} = \frac{1}{v} - \frac{1}{2v}}$

$\bf{ \frac{1}{f} = \frac{2 - 1}{2v}}$

$\bf{ \frac{1}{f} = \frac{1}{2v}}$
$\bf{f = 2v} ...........(1)$


let image distance be same

second case


$\bf \: \frac{mi}{mu} = \frac{ - v }{u '}$

$\bf{ \frac{1}{3} = \frac{ - v}{ u'}}$

$\bf{u'=-3v}$


HENCE SOLVED

THANKS