In the displacement method, a convex lens is placed between an object and a screen. If the magnifications in the two positions are m₁ and m₂ (m₂ > m₁), the distance between the two positions of the lens is x. The focal length of the lens is:
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Question

In the displacement method, a convex lens is placed between an object and a screen. If the magnifications in the two positions are m₁ and m₂ (m₂ > m₁), the distance between the two positions of the lens is x. The focal length of the lens is:

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: Use the thin-lens formula 1/f = 1/v - 1/u with m = v/u. For lens material/medium changes use the lens-maker relation with the relative refractive index; powers of thin lenses in contact add. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is x/(m₁ - m₂). Therefore the correct option is B.

In the displacement method, a convex lens is placed between an object and a screen. If the magnifications in the two positions are m₁ and m₂ (m₂ &gt; m₁), the distance between the two positions of the lens is x. The focal length of the lens is:

In the displacement method, a convex lens is placed between an object and a screen. If the magnifications in the two positions are m₁ and m₂ (m₂ > m₁), the distance between the two positions of the lens is x. The focal length of the lens is: