10th Class Science Solved Paper - Science-2017 Delhi Set-I

  • question_answer An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.

    Answer:

    Given:   \[u=-15\text{ }cm,\text{ }f=-10\text{ }cm,\,\,{{h}_{i}}=4\,cm\]  
    Using the mirror formula
                \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\]
                \[\frac{1}{v}-\frac{1}{15}=\frac{-1}{10}\]
                \[\frac{1}{v}=\frac{-1}{10}+\frac{1}{15}\]
                \[\frac{1}{v}=\frac{-15+10}{150}=\frac{-5}{150}\]
                \[v=-30\,cm\]
    Thus, to obtain a sharp image of the object, the screen should be placed in front of the mirror at a distance of 30 cm.
    Now,            \[m=\frac{-v}{u}=\frac{\text{height of image}}{\text{height of object}}\]
                            \[m=-\left( \frac{-30}{-15} \right)\]\[\Rightarrow m=-2\]
                            \[-2=\frac{{{h}_{1}}}{4}\] \[\Rightarrow {{h}_{1}}=-8\,cm\]
                ‹         Height of the image is 8 cm.
     


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