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# An Object 2 Cm Tall Stands on the Principal Axis of a Converging Lens of Focal Length 8 Cm. Find the Position, Nature and Size of the Image Formed If the Object Is: (I) 12 Cm from the Lens - CBSE Class 10 - Science

ConceptRefraction of Light Image Formation by Lenses - Concave Lens

#### Question

An object 2 cm tall stands on the principal axis of a converging lens of focal length 8 cm. Find the position, nature and size of the image formed if the object is:
(i) 12 cm from the lens
(ii) 6 cm from the lens
State one practical application each of the use of such a lens with the object in position (i) and (ii).

#### Solution

Converging lens is a convex lens

Given:
Focal length (f) = +8 cm
Height of the object (h) = +2

(a)
(i) Object distance (u) =-2

Lens formula is given as:

1/f=1/v-1/u

1/8=1/v-1/-12

1/8=1/v+1/12

1/v=1/8-1/12

1/v=(3-2)/24

1/v=1/24

v=24 cm

Image is at a distance of 24 cm from the convex lens; therefore, we have:
Magnification =v/u

Magnification (m) =24/-12

m =-2

Hence, the image is real and inverted.

(b) Object distance (u)=-6

According to lens formula:

1/f=1/v-1/u

1/8=1/v-1/-6

1/8=1/v+1/6

1/8-1/6=1/v

(3-4)/24=1/v

-1/24=1/v

v=-24 cm

Image is at a distance of 24 cm in front of the lens; therefore , we have :

Magnification (m) =v/u

m=(-24)/-6

m=4

m=h_i/h_o

m=h_i/2

h_i=2xx4

h_i=8 cm

Height of the image is 8 cm.

Here, height is positive; therefore, image is virtual and erect.

The practical application for case (1) is that it can be used as a corrective lens for a farsighted person and for case (2), it can be used as a magnifying lens for reading purposes.

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Solution An Object 2 Cm Tall Stands on the Principal Axis of a Converging Lens of Focal Length 8 Cm. Find the Position, Nature and Size of the Image Formed If the Object Is: (I) 12 Cm from the Lens Concept: Refraction of Light - Image Formation by Lenses - Concave Lens.
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