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Q. An object of height 8 cm is placed in front of a lens. It's inverted image of height 4.8 cm is formed on the screen. If the focal length of the lens is 12 cm then by drawing at scale calculate the object distance, image distance and magnification.

Taking scale as 1cm = 4cm I've drawn the principal axis and the lens and marked focus (F) at 3cm from the lens. But how do I proceed from here with only the heights of the object and image?!

graph

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Do you know how to draw the image of an object set at a certain distance from the lens? It is sort of the inverse. Start by drawing the ray parallel to the optical axis from the object incident onto the lens and refracted through the focus $F$.

enter image description here

Extend both rays as much as you can (line in blue). Then, from the optical axis on the image side, find the perpendicular length of image that corresponds to the image length (the base is the focal axis and the tip of the image is where the image meets the refracted ray initially drawn).

Once you have it, join this point to the optical centre (the centre of the lens) and extend this ray (in purple) to meet the original incidence ray. Where they meet is where the object is.

You then have to measure the distances of the object, and of the image.

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If you know the height of the object, you can draw a ray that is parallel to the optical axis. And you should know how that gets refracted from the lens. Similarly, if you know the height of the (inverted!) image you can draw a ray parallel to the optical axis that will (now propagating in the opposite direction) get refracted by the lens. Now, these two rays are enough for you because at their intersections you get both the object and the image.

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