$A$ concave lens and a convex lens have the same focal length of $20 \ cm$ and are placed in contact. This combination is used to view an object $5 \ cm$ long kept at $20 \ cm$ from the lens combination. As compared to the object,the image will be:

  • A
    Magnified and inverted
  • B
    Reduced and erect
  • C
    Of the same size and erect
  • D
    Of the same size and inverted

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$A$ lens maker has to design an achromatic combination of effective power $-0.5 \, D$. The two types of glasses to be used (say $A$ and $B$) have dispersive powers in the ratio $\omega_A : \omega_B = 3 : 5$. Then the lens made from glass $A$ will have a focal length of ....... $cm$.

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$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave lens of focal length $20 \ cm$. An object is placed at $20 \ cm$ to the left of this lens system. The distance of the image from the lens in $cm$ is . . . . . .

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An object is located $4 \ m$ from the first of two thin converging lenses of focal lengths $2 \ m$ and $1 \ m,$ respectively. The lenses are separated by $3 \ m$. The final image formed by the second lens is located from the source at a distance of (in $m$):

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