A concave lens forms the image of an object such that the...

A concave lens forms the image of an object such that the distance between the object and the image is $10 \mathrm{~cm}$ and the magnification produced is $(1 / 4)$, the focal length of lens will be $\mathrm{cm}$
(A) - 6.2
(B) $-12.4$
(C) $-4.4$
(D) $-8.8$

Key Concepts

Lens Formula

The lens formula, 1/f = 1/v - 1/u (or its variations), connects the focal length (f) of a lens with the object distance (u) and the image distance (v). It is fundamental in analyzing how lenses form images and determining unknown parameters when two of the three quantities are known.

Magnification

Magnification in lens systems is defined as the ratio of the height (or size) of the image to the height of the object, which can also be expressed as the ratio of the image distance to the object distance. This concept helps in understanding the scaling (enlargement or reduction) of images produced by lenses.

Optical Sign Conventions

Sign conventions in optics are critical for applying formulas correctly. They determine the positive or negative nature of the object distance, image distance, and focal length. Consistent application of these conventions allows one to properly identify whether an image is real or virtual and whether it is formed on the same side or opposite side of the lens relative to the object.

Properties of Concave Lenses

Concave lenses are known for producing virtual, erect, and diminished images regardless of the object's position relative to the lens. Their focal length is always negative under the standard sign conventions, and understanding their behavior is essential for solving problems related to image formation in diverging optical systems.

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