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Question: A convex lens has focal length \(20cm\). Calculate at what distance from the lens should the object ...

A convex lens has focal length 20cm20cm. Calculate at what distance from the lens should the object be placed so that it forms an image at 40cm40cm on the other side of the lens. State the nature of the image formed.

Explanation

Solution

Recall that convex lens is the lens that is thicker at the center and thinner at the upper and lower edges. When the rays of light travel parallel to the principal axis of the convex lens, then it converges all the rays to a single point. The convex lens is also known as a converging lens.

Complete answer:
Step I:
Given that the focal length of the lens is f=20cmf = 20cm
The distance of image is v=40cmv = 40cm
Distance of the object u=?u = ?
Nature of image=?
Step II:
The relation between distance of the object, image and the focal length of the lens can be written by using lens formula. The lens formula is
⇒1f=1v−1u\Rightarrow \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}
Substituting all the given values in the equation and solving,
⇒120=140−1u\Rightarrow \dfrac{1}{{20}} = \dfrac{1}{{40}} - \dfrac{1}{u}
⇒1u=140−120\Rightarrow \dfrac{1}{u} = \dfrac{1}{{40}} - \dfrac{1}{{20}}
⇒1u=1−240\Rightarrow \dfrac{1}{u} = \dfrac{{1 - 2}}{{40}}
⇒1u=−140\Rightarrow \dfrac{1}{u} = - \dfrac{1}{{40}}
Therefore the distance of the object is
⇒u=−40cm\Rightarrow u = - 40cm
Step III:
The nature of the image formed can be known by using the formula of magnification. The formula can be written as
⇒m=vu\Rightarrow m = \dfrac{v}{u}
Substituting the values and solving, the value of magnification is
⇒m=40−40\Rightarrow m = \dfrac{{40}}{{ - 40}}
⇒m=−1\Rightarrow m = - 1
Since the value of magnification is negative, therefore, the image formed will be real inverted and will be formed on the same side on which the object is placed.

Note:
It is important to note that the magnification of an optical instrument is helpful in knowing the nature and type of the image formed. By knowing the value of magnification, it can be known how enlarge an image can be formed. It is defined as the ratio of the height of the image to the height of the object. Also it can be expressed in terms of image and object distance.