10th Class Science Solved Paper - Science-2016 Outside Delhi Set-I

  • question_answer 23)
    (a) Define optical centre of a spherical lens.
    (b) A divergent lens has a focal length of 20 cm. At what distance should an object of height 4 cm from the optical centre of the lens be placed so that its image is formed 10 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.

    Answer:

    (a) Optical centre is a point on a lens through which ray of light passes undeviated, without suffering any refraction.
    (b) Given: \[f=\text{ }20\text{ }cm,\text{ }{{h}_{0}}=4\,cm,\text{ }v=\,\,10\,cm\]
                We know that,
                            \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]
                            \[\frac{1}{-20}=-\frac{1}{10}-\frac{1}{u}\]
                            \[\frac{1}{u}=-\frac{1}{10}+\frac{1}{20}\]
                            \[\frac{1}{u}=-\frac{-2+1}{20}=\frac{-1}{20}\]
                            \[u=-20cm\]
                Now,     \[m=\frac{hi}{ho}=\frac{v}{u}\]
                            \[\frac{hi}{4}=\frac{-10}{-20}\]
                             \[2{{h}_{i}}=4\]
    \[\Rightarrow \]               \[{{h}_{i}}=2\mathrm{cm}\]                            


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