Question

$\Large\mathcal{\fcolorbox{lime}{black}{\pink{Question}}}$

#An object is placed at a distance of 12 cm from a convex mirror of radius of curvature 12 cm.Find the position of the image.....

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Answer 1

Given:

• u = - 12cm.

• r = 12cm.

• f = 12/2 = 6cm.

To Find:

• Position of image (v) = ?

Formula Used:

$\star \: \boxed{\sf\red{ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} }}$

Solution:

$\sf\underline{\bigstar \: According \: to \: question,}$

$:\implies\mathfrak{ \frac{1}{6} = \frac{1}{v} + (\frac{ - 1}{12} ) } \\ \\ :\implies\mathfrak{ \frac{1}{6} + \frac{1}{12} = \frac{1}{v} } \\ \\ :\implies\mathfrak{ \frac{2 + 1}{12} = \frac{1}{v} } \\ \\ :\implies\mathfrak{\dfrac{\cancel{3}}{\cancel{12}} = \frac{1}{v} } \\ \\ :\implies\rm{\underline{\boxed{\rm{v = 4 \: cm}}}} \: \bigstar$

Thus,

$\therefore\;{\underline{\sf{Position\; of\;image\;is\; \bf{4\;cm}.}}}$

Answer 2

Explanation:

A convex mirror ALWAYS produces a VIRTUAL, DIMINISHED image which is, NECESSARILY, observed INSIDE the mirror. The image is ALWAYS BEYOND the POLE of the mirror and ALWAYS < f.

The focal length of CONVEX mirrors is NEGATIVE. Then f = - 15 cm.

Use the mirror equation (properly):

(- 1/15) = (1/12) + (1/Di) → Di = NEGATIVE 20/3. The negative sign indicates that the image is VIRTUAL as it should be. Note also that Di < f, as it should be, and note also Di is DIMINISHED as it should be.

The image given by a convex mirror CAN NEVER be in front of the mirror as two of the answers lead you to believe.