Where should an object be placed in front of a convex lens of focal length 20cm so as to obtain a two times magnified image?

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Concept:

Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.

Convex lens: ​A lens having two spherical surfaces, bulging outwards is called a double convex lens (or simply convex lens).

• It is thicker in the middle as compared to the edges.
• Convex lenses converge light rays and hence, convex lenses are also called converging lenses.

The lens formula is:

\(\frac{1}{{\rm{v}}} - \frac{1}{{\rm{u}}} = \frac{1}{{\rm{f}}}\)

Magnification

\(m = \frac v u\)

Where, v = Distance of image, u = Distance of object, f = Focal length

Calculation:

Given:

u = - 30 cm, f = 20 cm

Using, \(\frac{1}{{\rm{v}}} - \frac{1}{{\rm{u}}} = \frac{1}{{\rm{f}}}\)

\(\frac{1}{{\rm{v}}} - \frac{1}{{\rm{-30}}} = \frac{1}{{\rm{20}}}\)

v = 60 cm

Maginfication

\(m = \frac v u\)

\(m = \frac {60}{30}\)

m = 2

• The image formed by the convex lens are:

• When the object is placed in between the focus and the pole of the converging lens, the image is formed beyond the focus on the same side of the lens as the object and the nature of the image is virtual, erect, and magnified. 
• Here the focal length of the convex lens is 10 cm, therefore to obtained the magnified image, the object distance should be less than 10 cm, and out of all options, 7 cm is smaller than 10 cm. 
• Therefore the object should be placed at a distance of 7 cm from the connex lens, so that this convex lens may act as a magnifying glass.

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CBSE 10 - Physics

Asked by topperlearningforcontent | 02 Feb, 2022, 03:32: PM

Text Solution

Solution : When the image formed by a convex lens, inverted and same size as the object, then the distance of the object from the lens is 2f (twice the focal length). Here, <br> Focal length, f=20 cm <br> So, `2f= 2 xx 20` cm <br> =40 cm <br> Thus, the object should be placed at a distance of 40 cm in front of the convex lens. (Please draw the ray diagram yourself).

The focal length of concave mirror is 20 cm. where should an object be placed to get an image magnified twice?

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