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# The focal length of a concave lens is $10 \mathrm{cm} .$ What should be the object distance in order that the image is $1 / 5^{\text {th}}$ of size of the object. Where is the image? What is its lateral magnification?

Last updated date: 13th Jun 2024
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Hint: It is known that a concave lens is a lens that possesses at least one surface that curves inwards. It is a diverging lens, meaning that it spreads out light rays that have been refracted through it. A concave lens is thinner at its centre than at its edges, and is used to correct short-sightedness. A lens is a transmissive optical device that disperses or focuses a light ray by means of refraction. A concave lens is also called a negative lens or a diverging lens. There are numerous uses of the concave lens, like in telescopes, cameras, lasers, glasses, binoculars, etc. A concave mirror can form both real, inverted images of various sizes and virtual, erect and enlarged images depending on the position of the object whereas a concave lens forms only virtual, diminished and erect images for all positions of the object.

We know that,
height i image $=I$
height $\%$ object $=0$
image distance $=\mathrm{V}$
object distance $=v$
given; $\dfrac{I}{0}=\dfrac{1}{5}$
hence, $\dfrac{v}{u}=\dfrac{1}{5}$
$v=\dfrac{u}{5}$
We know
$\dfrac{I}{0}=\dfrac{V}{u}=m$
from tans formulae we get,
$\Rightarrow$ $\dfrac{1}{6}=\dfrac{1}{v}-\dfrac{1}{u}$
$\Rightarrow$$\dfrac{1}{-10}=\dfrac{1}{(4 / 5)}-\dfrac{1}{u} \Rightarrow$$\dfrac{1}{-10}=\dfrac{5}{u}-\dfrac{1}{u}$
$\Rightarrow$$\dfrac{1}{-10}=\dfrac{4}{u}$
$v=-40$
Therefore, the lateral magnification is -40. Therefore, the lateral magnification is -40. Lateral magnification refers to the ratio of image length to object length measured in planes that are perpendicular to the optical axis. A negative value of linear magnification denotes an inverted image i.e., we must keep away from lam.

i.e., we must keep $40 \mathrm{cm}$ away from lam.

Note We know that focal length, usually represented in millimetres (mm), is the basic description of a photographic lens. The longer the focal length, the narrower the angle of view and the higher the magnification. The shorter the focal length, the wider the angle of view and the lower the magnification. The primary measurement of a lens is its focal length. The focal length of a lens, expressed in millimetres, is the distance from the lens's optical center (or nodal point) to the image plane in the camera. Focal length can also change the perspective and scale of your images. A lens with a shorter focal length expands perspective, giving the appearance of more space between the elements in our photo. Meanwhile, telephoto lenses tend to stack elements in the frame together to compress perspective.