A concave lens of focal length f forms an image which is n times the size of the object. What is

step 1 In this question we have a focal lens a concave lens concave lens of focal length is equal to f

A concave lens of focal length f forms an image which is n...

A concave lens of focal length $\mathrm{f}$ forms an image which is n times the size of the object. What is the distance of the object from the lens? (A) $(1+\mathrm{n}) \mathrm{f}$ (B) $(1-\mathrm{n}) \mathrm{f}$ (C) $[(1-\mathrm{n}) / \mathrm{n}] \mathrm{f}$ (D) $[(1+\mathrm{n}) / \mathrm{n}] \mathrm{f}$

A concave lens of focal length $\mathrm{f}$ forms an image which is n times the size of the object. What is the distance of the object from the lens?
(A) $(1+\mathrm{n}) \mathrm{f}$
(B) $(1-\mathrm{n}) \mathrm{f}$
(C) $[(1-\mathrm{n}) / \mathrm{n}] \mathrm{f}$
(D) $[(1+\mathrm{n}) / \mathrm{n}] \mathrm{f}$

Key Concepts

Virtual Image Formation

Concave lenses always form images that are virtual, meaning they cannot be projected onto a screen and are located on the same side of the lens as the object. This concept is important for understanding how the sign conventions and magnification formula are applied in optical calculations involving such lenses.

Lens Formula

The lens formula (1/f = 1/do + 1/di) is a fundamental relation in optics that connects the object distance (do), the image distance (di), and the focal length (f) of a thin lens. It is crucial for determining the characteristics of the image formed by the lens, such as its location and nature (real or virtual).

Focal Length and Sign Conventions

In optics, the focal length of a lens is signed according to the lens type. For concave (diverging) lenses, the focal length is negative, which reflects their property of forming virtual images. Correct use of sign conventions is essential for accurately applying the lens formula.

Magnification

Magnification is defined as the ratio of the height (or size) of the image to the height (or size) of the object, and it can also be expressed as the ratio of the image distance to the object distance (m = di/do). In the context of a concave lens, magnification, often a positive number due to the upright nature of virtual images, connects the physical size of the object to that of the image.

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