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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 38

  • question_answer
    An upright object is placed at a distance in front of a converging lens equal to twice the focal length \[20cm\]of the lens. On the other side there is a concave mirror of focal length \[15cm\] separated from the lens by a distance of \[70cm\]. Then select the correct statements from the following.
    (i) Magnification for the system is \[+1\]
    (ii) Magnification for the system is \[-1\]
    (iii) Final image by the system will be real and at distance of \[110\text{ }cm\]from centre of curvature of spherical mirror
    (iv) Final image by the system will be real and at distance of \[60\text{ }cm\]from centre of curvature of spherical mirror
    The correct statement is

    A) (i) and (iv)                     

    B) (ii) and (iii)         

    C) (i) and (iii)                     

    D) (ii) and (iv)

    Correct Answer: B

    Solution :

    [b] For the 1st refraction through the lens \[\frac{1}{v}+\frac{1}{40}=\frac{1}{20}\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{1}{40}=\frac{1}{40}\Rightarrow v=40cm\] Distance of this image from the mirror is \[d=7040=30,\]i.e. the centre of curvature of the mirror, therefore ray retraces its path and image coincides with the object, and it will be inverted. Hence final image will be at distance \[40\text{ }cm+70\text{ }cm=110\text{ }cm\]from the mirror.  


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