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CBSE Class 10 Science 2016 Term II Outside Delhi Set 1

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Question : 23 of 36
Marks: +1, -0
(a) Define optical centre of a spherical lens.
(b) A divergent lens has a focal length of 20 cm\text{cm}. At what distance should an object of height 4 cm4\text{ cm} from the optical centre of the lens be placed so that its image is formed 10 cm10\text{ cm} away from the lens. Find the size of the image also.
(c) Draw a ray diagram to show the formation of image in above situation.
Solution:  
(a) Optical centre is a point on a lens through which ray of light passes undeviated, without suffering any refraction.
(b) Given: f=−20 cm,h0=4 cm,v=−10 cmf=-20\text{ cm}, h_0=4\text{ cm}, v=-10\text{ cm} We know that,
  1f  =  1v−  1u  \;\frac{1}{f}\;=\;\frac{1}{v}-\;\frac{1}{u}\;
  −120  =−  110−  1u  \;-\frac{1}{20}\;=-\;\frac{1}{10}-\;\frac{1}{u}\;
  1u  =−  110+  120  \;\frac{1}{u}\;=-\;\frac{1}{10}+\;\frac{1}{20}\;
  1u  =  −2+120=  −120  \;\frac{1}{u}\;=\;\frac{-2+1}{20}=\;\frac{-1}{20}\;
u  =−20 cmu\;=-20\text{ cm}
Now,
m  =  hiho=  vu  m\;=\;\frac{h_i}{h_o}=\;\frac{v}{u}\;
  hi4  =  −10−20  \;\frac{h_i}{4}\;=\;\frac{-10}{-20}\;
⇒    \Rightarrow\;\; 2 h_i\;=4 \\ ⇒ h_i=2 {\cm}$
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