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10th Physics | Light | Linear Magnification Produced by Mirrors

Linear Magnification Produced by Mirrors

 

    The linear magnification produced by a spherical mirror (concave or convex) is defined as the ratio of the height of the image (h¢) to the height of the object (h). It is a pure ratio and has no units. It is denoted by the letter ‘m’ and is given by

\displaystyle \text{linear}\ \text{magnification}\ (m)=\frac{\text{height}\ \text{of}\ \text{the}\ \text{image}\ \text{({h}')}}{\text{height}\ \text{of}\ \text{the}\ \text{object}\ \text{(h)}}

or

\displaystyle m\,\,\,\,=\,\,\,\frac{{{h}'}}{h}\,

 

    The linear magnification ‘m’ is also related to the object distance (u) and image distance (v). It can be expressed as :

    Linear Magnification,         \displaystyle m=-\frac{v}{u}

    Þ    Linear magnification,         \displaystyle m\,\,\,\,=\,\,\,\frac{{{h}'}}{h}\,\,\,=\,\,\,-\,\,\frac{v}{u}

    This shows that the linear magnification produced by a mirror is also equal to the ratio of the image distance (v) to the object distance (u) with a minus sign.

 

LINEAR MAGNIFICATION IN CASE OF CONCAVE MIRROR

 

(i) For real and inverted image: According to the New Cartesian Sign Convention, for the real and inverted images formed by a concave mirror,

    object height (h) is always +ve

    image height (h¢) is always –ve

    \    Linear magnification, \displaystyle m=\frac{{{h}'}}{h}

         \displaystyle m=\frac{-ve}{+ve}     or \displaystyle m=-ve.

(ii) For virtual and Erect image : According to the new Cartesian sign convention, for the virtual and erect images formed by a concave mirror,

    object height (h) is always +ve

    image height (h¢) is always +ve.

    \    Linear magnification, \displaystyle m=\frac{{{h}'}}{h}

        \displaystyle m=\frac{+ve}{+ve} or \displaystyle m=+ve.

 

Note: In case of a concave mirror, for the real and inverted images the magnification is always –ve. and for the virtual and erect images the magnification is always +ve.

 

LINEAR MAGNIFICATION IN CASE OF CONVEX MIRROR

 

        A convex mirror always forms a virtual and erect image.

    (i) For virtual and erect image : According to the New Cartesian Sign Convention, for the virtual and erect images formed by a convex mirror,

        Object height (h) is always +ve

        Image height (h¢) is always +ve

        \    Linear magnification,     \displaystyle m=\frac{{{h}'}}{h}

        or    \displaystyle m=\frac{+ve}{+ve}

        or    \displaystyle m=+ve.

 

Note: In case of a convex mirror, which always form virtual and erect images, the magnification is always +ve.

 

FOR SPHERICAL MIRRORS IF THE

 

    (i)     Linear magnification, m > 1

        the image is enlarged i.e. greater than the object

    (ii)    Linear magnification, m = 1

        the image is of the same size as the object.

    (iii)    Linear magnification, m < 1

        The image is diminished i.e. the image is smaller than the object.

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