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A Diverging Mirror of Radius of Curvature 40 Cm Forms an Image Which is Half the Height of the Object. Find the Object and Image Positions. - Science

A diverging mirror of radius of curvature 40 cm forms an image which is half the height of the object. Find the object and image positions.

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Solution

Given,
The mirror is convex.
Magnification 'm' = 12
Radius of curvature 'R' = 40 cm
Focal length of the convex mirror 'f=2 = 20 cm`
We have to find the position of the image 'v' and distance of the object from the mirror 'u'.
Using the mirror formula, we get  
`1/f=1/u+1/v`
Given, m=`1/2` 
Again, m =`-v/u` 
Therefore,V =-`-1/2u` 
By puting the value of `V` in the mirror formula, We get  
`1/f=1/u-2/u(-1)/u` 
⇒`1/20=(-1)/u` 
⇒`u=-20cm` 
⇒`v=-((-20))/2` 
⇒`v=10 cm` 
If an objet is placed at a distance of 20 cm in front of the mirror, the image will be formed 10 cm behind the mirror.   

Notes

`1/f=1/u-2/u(-1)/u` 
⇒`1/20=(-1)/u` 
⇒`u=-20cm` 
⇒`v=-((-20))/2` 
⇒`v=10 cm` 

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APPEARS IN

Lakhmir Singh Class 10 Physics (Science)
Chapter 4 Reflection of Light
Q 7 | Page 209
Lakhmir Singh Class 10 Physics (Science)
Chapter 4 Reflection of Light
Q 7 | Page 209
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