A converging lens forms an image of an 8.00 m m tall real object. The image is 1
ID: 2124034 • Letter: A
Question
A converging lens forms an image of an 8.00 mm tall real object. The image is 11.5cm to the left of the lens, 3.50cm tall, and erect.What is the focal length of the lens? (cm)Where is the object located?(cm)style="color: rgb(51, 51, 51); font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px;">style="color: rgb(51, 51, 51); font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px;">style="color: rgb(51, 51, 51); font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(244, 249, 255);">style="display: inline-block; position: static; border-width: 0px; border-left-style: solid; padding: 0px; margin: 0px; vertical-align: -1.2px; overflow: hidden; width: 0px; height: 9.2px;">style="display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 44px;">class="mi" id="mathjax-span-22">class="mi" id="mathjax-span-21">class="mrow" id="mathjax-span-20">class="texatom" id="mathjax-span-19">class="mrow" id="mathjax-span-18">style="position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(34px 15600px 47.2px -8.5px); top: -44px; left: 0px;">style="display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 20px; height: 0px; font-size: 16px;">style="border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; vertical-align: 0px;">class="mathjax" id="mathjax-element-3-frame" role="textbox" aria-readonly="true">class="mathjax_preview">class="type-specific" type="tex">class="replace-insert done" inserttype="units" id="yui_3_3_0_24_137628959985143">style="color: rgb(51, 51, 51); font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(244, 249, 255);">style="display: inline-block; position: static; border-width: 0px; border-left-style: solid; padding: 0px; margin: 0px; vertical-align: -1.2px; overflow: hidden; width: 0px; height: 9.2px;">style="display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 44px;">class="mi" id="mathjax-span-16">class="mi" id="mathjax-span-15">class="mrow" id="mathjax-span-14">class="texatom" id="mathjax-span-13">class="mrow" id="mathjax-span-12">style="position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(34px 15600px 47.2px -8.5px); top: -44px; left: 0px;">style="display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 20px; height: 0px; font-size: 16px;">style="border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; vertical-align: 0px;">class="mathjax" id="mathjax-element-2-frame" role="textbox" aria-readonly="true">class="mathjax_preview">class="type-specific" type="tex">class="replace-insert done" inserttype="units" id="yui_3_3_0_24_137628959985139">style="color: rgb(51, 51, 51); font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(244, 249, 255);">style="display: inline-block; position: static; border-width: 0px; border-left-style: solid; padding: 0px; margin: 0px; vertical-align: -1px; overflow: hidden; width: 0px; height: 8.9px;">style="display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 44px;">class="mo" id="mathjax-span-10">class="mspace" id="mathjax-span-9">class="mi" id="mathjax-span-8">class="mi" id="mathjax-span-7">class="mspace" id="mathjax-span-6">class="mo" id="mathjax-span-5">class="mrow" id="mathjax-span-4">class="texatom" id="mathjax-span-3">class="mrow" id="mathjax-span-2">style="position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(34.1px 15600px 47px -7.7px); top: -44px; left: 0px;">style="display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 59px; height: 0px; font-size: 16px;">style="border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; vertical-align: 0px;">class="mathjax" id="mathjax-element-1-frame" role="textbox" aria-readonly="true">class="mathjax_preview">class="type-specific" type="tex">class="replace-insert done" inserttype="units" id="yui_3_3_0_24_137628959985128">style="color: rgb(51, 51, 51); font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px; background-color: rgb(244, 249, 255);">
Explanation / Answer
m = hi/ho = - di /do
For the above formula the following sign conventions are used.
%u2022 f is + if the lens is a double convex lens (converging lens)
%u2022 f is - if the lens is a double concave lens (diverging lens)
%u2022 di is + if the image is a real image and located on the opposite side of the lens.
%u2022 di is - if the image is a virtual image and located on the object's side of the lens.
%u2022 hi is + if the image is an upright image (and therefore, also virtual)
%u2022 hi is - if the image an inverted image (and therefore, also real)
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In this problem
%u2022 hi is + if the image is an upright image (and therefore, also virtual)
%u2022 di is - if the image is a virtual image and virtual image is located on the object's side of the lens.
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M = -di/do = hi / ho
-11.5 cm/do = 3.5cm/8mm
-11.5cm/do = 35 mm/ 8 mm
-11.5 / do = 4.3
do = -2.624 cm
1 /f = 1/obj + 1/img
= 1/2.624 + 1/-11.5
f = 3.40 cm
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