Question

At what distance does an object have to be placed in order to obtain the real image whit the size same as an object with the help of convex lens ? 1️⃣F1 , 2️⃣ optical center ,3️⃣2F1, 4️⃣2F2​

Answer 1

Answer:

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$\huge\mathcal{\green{3) \ 2F1}}$

Explanation:

When we place an object at C1 or 2F1 of the convex lens, then we obtain an image. The size of the obtained image is same as the object. The image obtained is formed at 2F2 or C2 . The image formed is real and inverted.

Note:-

Objects are always placed at the left side of the lens according to the sign convention.

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Answer 2

The answer is (3)2F1.

Given: The lens is convex

The image is real and of the same size as the object

To Find: Position of the object

Solution:

A convex lens is converging in nature. A ray of light parallel to the principal axis passes through the focus after refraction.

As a convention, we assume that the light ray strikes from the left side. The focus on the left side is named F1 and that on the right side is named F2. The left side is considered negative and the right side is positive.

Magnification is given as

m = - v / u, where m is the magnification, u is the distance of the object from the lens and v is the distance of the image from the lens.

Since the image is real the magnification will be negative.

Since the image is having the same size as the object, the magnification will be 1

m = -1

- 1 = -v/u

v = u                     ..1

The object is placed on the left side so u is negative

The lens formula is given as

$\frac{1}{v}- \frac{1}{-u} = \frac{1}{f}$

$\frac{1}{u} + \frac{1}{u} = \frac{1}{f}$

2/ u = 1/ f

u = 2f

So, the object must be placed at a distance of 2f from the lens on the left side.

Therefore, the answer is (3)2F1.