A real and inverted image of the same size is formed by a convex lens when the object is placed

There are six possibilities of position of object in the case of convex lens:

Object at infinity:

Convex lens converge parallel rays coming from objet at infinity and a highly diminished - point sized, real and inverted image is formed at principal focus F2.

Fig: Object at Infinity

Properties of Image: Image is highly diminished, real and inverted.

Object beyond C1 or 2F1Centre of Curvature

A diminished, real and inverted image is formed between principal focus, F2 and centre of curvature, C2 at the opposite side when an object is placed beyond C1 of a convex lens.

Fig: Object Beyond 2F

Properties of Image: Image is diminished, real and inverted.

Object at CCentre of Curvature

A same sized, real and inverted image is formed at centre of curvature, C2 when object is placed at centre of curvature, C1 of a convex lens.

Fig: Object at 2F

Properties of Image: Image is same size as object, real and inverted.

Object between C and F

An enlarged, real and inverted image is formed beyond centre of curvature, C2 when an object is placed between centre of curvature, C1 and principal focus, F1 of a convex lens.

Fig: Object between 2F and F

Properties of Image: Image is enlarged, real and inverted.

Object at Focus F1

An infinitely large, real and inverted image is formed at infinity when object is placed at principal focus, F1 of a convex lens.

Fig: Object at F

Properties of Image: Image is highly enlarged, real and inverted.

Between F1 and O

A virtual, erect and enlarged image is formed at the same side of lens, when an object is placed between principal focus, F1 and optical centre, O of a convex lens.

Fig: Object between F and O

Properties of Image: Image is enlarged, virtual and erect.

Summary of Image Formation

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Option 3 : At twice the focal length

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CONCEPT:

• 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.
  • The lens whose refracting surface is upside is called a convex lens and the lens whose refracting surface is inside is called a concave lens or diverging lens.
  • The convex lens is also called a converging lens.

EXPLANATION:

• When the object is placed at twice the focal length distance from the optical center on the principal axis of a convex lens, a real and inverted image of the same size is obtained.

ALTERNATE SOLUTION:

Analytically,

• The focal length of the convex lens can be calculated by 

\(⇒ f = \frac{{m\left( {u + v} \right)}}{{{{(1 + m)}^2}}}\)

Where, m = magnification (in this case m = 1),

u = object distance,

v = image distance (in this case u = v), and

f = focal length

\(⇒ f = \frac{{1 \times \left( {u + u} \right)}}{{{{(1 + 1)}^2}}}\)

\(⇒ f = \frac{{2u}}{{{2^2}}}\)

⇒ u = 2f

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