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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. - Science

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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.

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Solution 1

Object distance, u = −25 cm
Object height, ho = 5 cm
Focal length, f = +10 cm
According to the lens formula,

`1/v-1/u=1/f`

`1/v=1/f+1/u=1/10-1/25=15/250`

`v=250/15=16.66 cm`

The positive value of v shows that the image is formed at the other side of the lens.

Magnification m =`-"image distance"/"object distance"=-v/u=16.66/25=-0.66`

The negative sign shows that the image is real and formed behind the lens.

Magnification m =`"image height"/"object height"=H_i/H_o=H_i/5`

Hi=m x Ho=-0.66 x 5=-3.3 cm

The negative value of image height indicates that the image formed is inverted.The position, size, and nature of image are shown in the following ray diagram.

 

Solution 2

Given:
Object distance, u =-25 cm
Focal length, f = 10 cm
Height of the object, h = 5 cm
Applying the lens formula, we get:

`1/f=1/v-1/u`

⇒`1/v=1/f+1/u`

⇒`1/v=1/f+1/u`

⇒`11/2/v=1/10+1/-25`

⇒`1/v=(5-2)/50`

⇒`1/v=3/50`

⇒`1/v=3/50`

⇒`v=50/3=+16.6 ` cm

The image will be at a distance of 16.6 cm behind the lens.

`m=v/u=50/3`

`m=h_i/h=50/3`

`m=h_i/h=h_i/5`

`h_i/5=(-2)/3`

h=(-10)/3=-3.3 cm

Thus, the image will be 3.3 high. It will be real and inverted

 

Concept: Convex Lens
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APPEARS IN

NCERT Class 10 Science
Chapter 10 Light – Reflection and Refraction
Q 10 | Page 186
Lakhmir Singh Class 10 Physics (Science)
Chapter 5 Refraction of Light
Q 16 | Page 247

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