If a convex lens of focal length $80 \ cm$ and a concave lens of focal length $50 \ cm$ are combined together,what will be their resulting power?

  • A
    $+6.5 \ D$
  • B
    $-6.5 \ D$
  • C
    $+7.5 \ D$
  • D
    $-0.75 \ D$

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If $\vec{a}, \vec{b}$ and $\vec{c}$ are vectors with magnitudes $2, 3$ and $4$ respectively,then the best upper bound of $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ among the given values is

A prism of angle $75^\circ$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index $1.5$ only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be . . . . . . .
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