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A Concave Mirror Has a Focal Length of 4 Cm and an Object 2 Cm Tall is Placed 9 Cm Away from It. Find the Nature, Position and Size of the Image Formed. - Science

A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature, position and size of the image formed. 

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Solution

Distance of the object from the mirror 'u' = −9cm
Height of the object 'ho' = 2 cm
Focal length of the mirror 'f' = −4 cm
We have to find the distance of the image 'v' and height of the image 'hi'.
Using the mirror formula, we get  

`1/f=1/v+1/u` 

`1/-4=1/v+1/-9` 

`1/-4=1/v-1/9` 

`1/9-1/4=1/v` 

`(4-9)/36=1/v`  

`-5/36=1/v=(-1)/7.2`  

v=7.2 cm 

Therefore, distance of the image 'v' is 7.2 cm.
Now, using the magnification formula, we get 

 `m=h_i/h_o=-v/u`  

`h_i/H_o=-((-7.2))/-9` 

`h_i/2=((-7.2))/-9` 

`h_-i=(2xx(-7.2))/9` 

`h_i=-1.6 cm`   

Thus, the height of the image 'hi' is 1.6 cm.
Again, using the magnification formula, we get 

`m=-v/u` 

`m=-(-7.2)/-9` 

m=-0.8  

Thus, the image is real, inverted and small in size.

  Is there an error in this question or solution?
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APPEARS IN

Lakhmir Singh Class 10 Physics (Science)
Chapter 4 Reflection of Light
Q 19 | Page 199
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