A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 30 cm. Find the position and nature of the image formed.

By Ritesh|Updated : November 8th, 2022

(a) Position of image = 60 cm, image is virtual and erect

(b) Position of image = - 60 cm, image is virtual and erect

(c) Position of image = 60 cm, image is real and inverted

(d) Position of image = 12 cm, image is real and inverted

A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 30 cm. The position and nature of the image formed are Positions of image = 60 cm, image is real and inverted. The correct options are (c) Position of image = 60 cm, image is real and inverted.

Step to Find the position and nature of the image formed

Given object size h = 5 cm

Object distance from lens u = − 30 cm

Focal length f = 20 cm (as per sign conventions)

We must determine the nature of the produced image and the image distance v.

Let hi be the height of the image.

Using the lens formula:

1/f = 1/v - 1/u

Putting the values we have,

1/20 = 1/v - 1/-30

1/20 - 1/30 = 1/v

1/v = (3 - 2)/ 60

v = 60 cm

We know, magnification, M = hi/h = v/u = hi/5 = 60/-30

hi = - 10 cm

According to sign norms, the image is actual and inverted because it forms near the right side of the lens and has a height of around 10 cm.

Lens Formula:

Concave lenses are known as diverging lenses because the rays diverge after falling on them, whereas convex lenses are also referred to as converging lenses because the rays converge after falling on them. Depending on their distance from the lens and their size, the images created by these lenses may be real or virtual. With the use of the lens formula, the image distance may be determined with the knowledge of object distance and focal length. The Lens formula in optics describes the relationship between the distance of an image I the distance of an object (o), and the focal length of the lens (f).

Summary:

A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 30 cm. Find the position and nature of the image formed.

A convex lens with a 20 cm focal length is placed perpendicular to a 5 cm tall object. 30 centimeters separate the object from the lens. The position and type of the created picture are Positions of the image is 60 cm, and it is both actual and upside-down.

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