Question

The linear magnification produced by a spherical mirror is -1/. analysing this value state th typical of sphere mirror and position of the object with respect to the power of the mirror

Answer 1

the magnification is -1 therefore it should be cocave mirror

Answer 2

Hope u like my process
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=> linear magnification is equal to the negative of the ratio of image distance to the object distance.

$i.e. \\ \: \blue{\it\: linea r \: \: magnification} = \bf - \frac{image \: \: distance}{object \: \: distance} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline{ \bf - \frac{v}{u} }$
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In optics..

=> use of sign convention is necessary..

So,

For convex mirror,
=-=-=-=-=-=-=-=-=-=-=
=> image distance (v) = (+) ve

=> object distance(u) = (-) ve

$= > its \: \: linear \: \: magnification = - \bf \frac{( + v)}{( - u)} = \underline{ \frac{v}{u} }$


For concave mirror,
=-=-=-=-=-=-=-=-=-=-=-=
=> image distance(v) = (-) ve

=> object distance(u) = (-) ve

$= > its \: \: linear \: \: magnification = \bf- \frac{( - v)}{( - u)} = \underline{ - \frac{v}{u} }$

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Now,
=-=-=-=
Given data:
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
=> linear magnification = - 1

So,

The linear magnification is (-)ve in concave mirror and hence concave mirror is used.
_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_

Now the magnitude of the magnification is 1.. So the object and image distance are same.

Image formation for concave be like

$\green{ \bf \underline{\: object \: \: distance} \: \: \: \underline{\: image \: \: distance}} \\ \\ \blue{ \: \: \: \: \: \: \: \: \: focus (f)\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: infinity }\\ \\ \blue{ \: \: \: \: \: \: \: \: \: \: infinity \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: focus(f)} \\ \\ \blue{\: \: \: \: \: \: \: \: radius (2f) \: \: \: \: \: \: \: \: \: \: \: radius(2f) }\\ \\ \blue{ \: \: \: \: \: \: pole < x < f\: \: \: \: \: \: \:focus < x < 2f} \\ \\ \blue{ \: \: \:focus < x < 2f \: \: \: \: \: \: \: \: pole < x < f\: \: }$


Thus the distance is same when object is placed at 2f(radius of curvature).

Thus the required answer is

Concave mirror is used with the object placed at a distance of 2f.
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Hope this is ur required answer

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