When an object is placed at 10 cm and 30 cm from a convex lens images obtained are of the same magnitude of magnification the focal length of the lens may be?

Text Solution

Solution : The convex lenses and the plane mirror as shown in figure. <br> The combination behaves like a concave mirror. <br> Let the distance of the object from the first lens be x. <br> For the ray to retrace its path, it should be incident normally on the plane mirror. <br> Form the diagrm, we see that for lens `L_(2)` <br> `v=oo, f=+10cm, u=?` <br> Form the lens equation, we get <br> `(1)/(v)-(1)/(u)=(1)/(f)` or `u=-10cm` <br> From the diagram, we see that for lens `L_(1)` <br> `v=30-10=20cm, f=+10cm, u=-x` <br> From the lens equation, we get <br> `(1)/(v)-(1)/(u)=(1)/(f)` or `(1)/(20)-(1)/(-x)=(1)/(10)` or `x=20cm` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/BMS_V04_C01_E01_119_S01.png" width="80%">

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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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