What is the nature of the image formed by a convex lens when the object is placed between 2F₂ and f₂?

An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.

Table of Contents Show

Object at infinity:
Object at CCentre of Curvature
Object at Focus F1
Summary of Image Formation

Converging lens means a convex lens. As the distances given in the question are large, so we choose a scale of 1: 5, i.e., 1 cm represents 5 cm. Therefore, on this scale 5 cm high object, object distance of 25 cm and focal length of 10 cm can be represented by 1 cm high, 5 cm and 2 cm lines respectively. Now, we draw the ray diagram as follows:(i) Draw a horizontal line to represent the principal axis of the convex lens.(ii) Centre line is shown by DE.(iii) Mark two foci F and F' on two sides of the lens, each at a distance of 2 cm from the lens.(iv) Draw an arrow AB of height 1 cm on the left side of lens at a distance of 5 cm from the lens.(v) Draw a line AD parallel to principal axis and then, allow it to pass straight through the focus (F') on the right side of the lens.(vi) Draw a line from A to C (centre of the lens), which goes straight without deviation.(vii) Let the two lines starting from A meet at A'.(viii) Draw AB', perpendicular to the principal axis from A'.(ix) Now AB', represents the real, but inverted image of the object AB.(x) Then, measure CB' and A'B'. It is found that CB' = 3.3 cm and A'B' = 0.7 cm.

(xi) Thus the final position, nature and size of the image A'B' are: (a) Position of image A'B' = 3.3 cm × 5 = 16.5 cm from the lens on opposite side. (b) Nature of image A’B’: Real and inverted.

(i) When the object is situated at infinity, the position of image is at F2, it is very much diminished in size and it is real and inverted.

(ii) When the object (AB) is situated beyond 2F1, the position of image (A'B') is between F2 and 2F2, it is diminished in size and real and inverted.

(iii) When the object (AB) is situated at 2F1, the position of image (A'B') is at 2F2, it is of same size as the object and real and inverted.

(iv)When the object (AB) is situated between 2F1and F1, the position of image (A'B') is beyond 2F2, it is magnified in size and real and inverted.

(v) When the object (AB) is situated at F1, the position of image is at infinity; it is very much magnified in size and real and inverted.

(vi) When the object (AB) is situated between lens and F1, the position of image (CD) is on the same side, behind the object; it is magnified in size and virtual and upright.

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State the changes in the position, size and nature of the image of an object when brought from infinity up to a concave lens. Illustrate your answer by drawing ray diagrams.

(i) When object (AB) is situated at infinity then parallel rays from object appears to fall on concave lens. Due to which image forms at focus. This image is highly diminished in size and virtual and upright

(ii) When object (AB) is situated at any point between infinity and optical centre of the lens then image forms between focus and optical centre. This image is diminished in size and virtual and upright.

Is there an error in this question or solution?

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.

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.

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.

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

Object at Infinity	Image is formed at focus. Image is real, inverted and highly diminished in size.
Beyond C	Image is formed between F2 and 2F2. Image is real, inverted and smaller than object.
Between C and F	Image is formed beyond C2 or 2F2. Image is real, inverted and larger than object.
At C	Image is formed at 2F2 or C2. Image is real, inverted and of same size as object.
At F	Image is formed at infinity. Image is real, inverted and highly enlarged.
Between F and O	Image is formed on 2F1. Image is virtual, erect and larger than object.