In the displacement method, a convex lens is placed in between an object and a screen. If the magnification in the two positions are, and and the distance between the two positions of the lens is , the focal length of the lens is,
Step 1. Given data
It is given that the magnification in the two positions are, and and the distance between the two positions of the lens is .
We have to find the focal length of lens.
Step 2. Formula to be used
The lens formula is,
Here, is the focal length measured in meter, is object distance and is image distance.
Step 3. Draw the figure which show image formation in the displacement method
We know in displacement method,
Let distance of the image from the lens , distance of the object from the lens be and magnification of the lens .
So the displacement formula is,
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and
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So,
Step 4. Find the focal length.
From the figure,
Given is,
Solve it by using lens formula is,
Here, is the focal length measured in meter, is object distance and is image distance.
So,
We know that, .
So,
Hence, option is correct answer.