CBSE Class 10 Science 2017 Delhi Term II Set 2 Paper

Question : 9 of 9

Marks: +1, -0

3 {\cm}

tall object is placed

18 {\cm}

in front of a concave mirror of focal length

12 {\cm}

. At what distance from the mirror should a screen be placed to see a sharp image of the object on the screen. Also calculate the height of the image formed.

Solution:

Using mirror equation :

u=-18 {\cm}, f=-12 {\cm}, v=?, h_1=+3 {\cm}, h_2=?

\;{1}/{v}+\;{1}/{u}=\;{1}/{f}

⇒ \;\; \;{1}/{v}-\;{1}/{18}\;=-\;{1}/{12}

\;{1}/{v}\;=-\;{1}/{12}+\;{1}/{18}

⇒ \;\; \;{1}/{v}\;=\;{-3+2}/{36}=\;{-1}/{36}

v\;=-36 {\cm}

Thus, to obtain a sharp image of the object, the screen should be placed at a distance of

36 {\cm}

, in front of the mirror.
Now,

m=\;{-v}/{u}=\;{h_2}/{h_1}

m=- (\;{-36}/{-18}) =-2

-2\;=\;{h_2}/{3}

h_2\;=-6 {\cm}

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