What is the focal length of convex lens positive or negative

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CONCEPT:

• Focal length: The distance from the lens to its focal point is called the focal length. 

The focal length of a lens is given by the lens maker formula:

\(\frac{1}{f}=(μ-1)(\frac{1}{R_1}-\frac{1}{R_2})\)

where f is the focal length of the lens, μ is the refractive index of the lens, and R1 and R2 are the radiuses of curvature.

• For converging lenses or convex lenses, the focal length is always positive.
• For diverging lenses or concave lenses, the focal length is always negative.

EXPLANATION:

• For the concave lens, the focal length is always negative.
• A concave lens diverges the rays incident on it and a convex lens converges the rays incident on it.
• We know that the focal length is in the negative x-direction for a concave lens while it is in the positive x-direction for the convex lens.
• So f is negative for a concave lens and positive for a convex lens.
• It is a sign convention.
• Hence the correct answer is option 1.

​

The Sign convention for spherical lenses are as follows:

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Is focal length of convex lens negative when it is surrounded by a medium with greater refractive index than that of lens?

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