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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

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Question

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.

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.   
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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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Chapter 4: Reflection of Light - Exercise 7 [Page 209]

APPEARS IN

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