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<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 1 over denominator f end fraction equals fraction numerator 1 over denominator v end fraction minus fraction numerator 1 over denominator u end fraction" width="89" height="37" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»v«/mi»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»u«/mi»«/mrow»«/mfrac»«/math»'/> (Given <img src="data:image/png;base64,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" class="Wirisformula" alt="u equals fraction numerator negative f over denominator 2 end fraction" width="56" height="36" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»u«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»-«/mo»«mi»f«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/>)<br /><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjwvbWF0aD5WOBRoAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⇒«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 1 over denominator f end fraction equals fraction numerator 1 over denominator v end fraction plus open parentheses fraction numerator 1 over denominator f divided by 2 end fraction close parentheses rightwards double arrow fraction numerator 1 over denominator v end fraction equals fraction numerator 1 over denominator f end fraction minus fraction numerator 2 over denominator f end fraction" width="228" height="39" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»v«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»f«/mi»«mo»/«/mo»«mn»2«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo»⇒«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»v«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mn»2«/mn»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/mfrac»«/math»'/><br /><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjwvbWF0aD5WOBRoAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⇒«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 1 over denominator v end fraction equals fraction numerator negative 1 over denominator f end fraction" width="66" height="37" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»v«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/mfrac»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="m equals fraction numerator v over denominator u end fraction equals fraction numerator f over denominator f divided by 2 end fraction equals 2" width="132" height="39" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»v«/mi»«/mrow»«mrow»«mi»u«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»f«/mi»«/mrow»«mrow»«mi»f«/mi»«mo»/«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»2«/mn»«/math»'/><br />So virtual at the focus and of double size.

An object is placed at a distance of <img src="data:image/png;base64,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" class="Wirisformula" alt="f over 2" width="18" height="36" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»f«/mi»«mn»2«/mn»«/mfrac»«/math»'/>from a convex lens. The image will be

Solution for the question - an object is placed at a distance of (f)/(2) from a convex lens. the imagewill be at 3_f_ / 2, real and inverted