Displacement method To know Focal length

Complete step-by-step solution:
This is the required set up of the experiment.

i)Ray diagram for displacement method to determine focal length -

Initially the lens L1 is placed at position 1 closer to the object AB and its position is so adjusted so that we get clear image A1B1 on the screen. The position of the lens and the distance between the object and the image is marked and noted.
Keeping the same distance between the object and image, the lens is now moved to a new position towards the screen in new position 2 and in this position lens is adjusted till a clear image is obtained on the screen. This position of the lens and distance between the object and image is marked and noted.
(ii) Formula Derivation : -Let us assume the distance between object and image is D.
Let us assume the distance between two positions of the lens is d.
This displacement method is based on principle on the reversibility of light, if the direction of a ray of light is reversed, it will follow the same path as that of the original path.
Hence, the distance of the object from the lens and that of the image from the lens can be interchanged and we still get a focused image.
We therefore get the two positions of the lens for getting a clear focused image of an object with the same distance between the object and image on both positions of object and image. In other words, the distance between the object and the lens in the first position is the same as the distance between the image and the lens in the second position and also, the distance between the image and the lens in the first position is the same as the distance between the object and lens in the second position.
Distance between object and lens is u.
Distance between image and lens is v.

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