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

Radius of curvature = R = 40 cm
We have to find the position of object and image.
Let U be the position of an object and V be the position of an image.
Then,
U = ?
V = ?
Also suppose that, h₁ and h₂ be the height of object and height of image respectively.
Then, according to the given condition, the height of image is half of the height of object.
Therefore, h₂ = h₁ / 2
Also, we know that,

$fraction numerator negative v over denominator u end fraction space equals space h subscript 2 over h subscript 1 fraction numerator negative v over denominator u end fraction space equals space fraction numerator open parentheses h subscript 1 divided by 2 close parentheses over denominator h subscript 1 end fraction fraction numerator begin display style negative v end style over denominator begin display style u end style end fraction space equals space 1 half 2 space v space equals space minus u v space equals space fraction numerator negative u over denominator 2 end fraction......... left parenthesis 1 right parenthesis n o w space w e space u s e space t h e space m i r r o r space f o r m u l a comma 1 over v plus 1 over u space equals space 1 over f 1 over v plus 1 over u space equals space 2 over R fraction numerator 1 over denominator negative u divided by 2 end fraction space plus 1 over u space equals space 2 over R u sin g space e q u a t i o n space left parenthesis 1 right parenthesis fraction numerator negative 2 over denominator u end fraction plus 1 over u space equals space 2 over 40 fraction numerator negative 1 over denominator u end fraction space equals space 1 over 20 u space equals space minus 20 c m n o w space v space equals space fraction numerator negative u over denominator 2 end fraction space equals space fraction numerator negative left parenthesis negative 20 right parenthesis over denominator 2 end fraction v space equals space 10 c m w h i c h space i s space t h e space r e q u i r e d space a n s w e r.$

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