Question #167251

A converging thin lens with 50cm focal lens forms area/image that is 2.5 times larger than the object. How Far is the object from the image.


1
Expert's answer
2021-02-28T07:34:06-0500

Let's write the magnification equation:


M=2.5hih0=did0,M=\dfrac{2.5h_i}{h_0}=-\dfrac{d_i}{d_0},2.5=did0,2.5=-\dfrac{d_i}{d_0},di=2.5d0.d_i=-2.5d_0.

Let's write the thin lens equation and find the object distance:


1do+1di=1f,\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},1do12.5do=1f,\dfrac{1}{d_o}-\dfrac{1}{2.5d_o}=\dfrac{1}{f},do=1.5f2.5=1.550 cm2.5=30 cm.d_o=\dfrac{1.5f}{2.5}=\dfrac{1.5\cdot50\ cm}{2.5}=30\ cm.

Then, we can find the image distance:


di=2.5d0=2.530 cm=75 cm.d_i=-2.5d_0=-2.5\cdot30\ cm=-75\ cm.

The sign minus indicates that the image is virtual and formed on the same side as the object.

Finally, we can find the distance from the object to the image:


d=dido=75 cm30 cm=45 cm.d=d_i-d_o=75\ cm-30\ cm=45\ cm.


Hence, the image formed 45 cm to the left from the object.


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