$A$ ray of light is incident at an angle '$i$' on one face of a thin angled prism. The ray emerges normally from the other face. If the refractive index of the glass prism is '$n$' and the angle of the prism is '$A$',then the value of '$i$' is:

  • A
    $An$
  • B
    $A^{2}n$
  • C
    $\frac{n}{A}$
  • D
    $\frac{1}{An}$

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$A$ prism of refractive index $n_{1}$ and another prism of refractive index $n_{2}$ are stuck together (as shown in the figure). $n_{1}$ and $n_{2}$ depend on $\lambda$, the wavelength of light, according to the relation:
${n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text{ and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}$
The wavelength for which rays incident at any angle on the interface $BC$ pass through without bending at that interface will be $....\,nm.$

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Given below are two statements :
Statement $I$ : When white light is passed through a prism,the red light bends less than yellow and violet light.
Statement $II$ : The refractive indices are different for different wavelengths in a dispersive medium.
In the light of the above statements,choose the correct answer from the options given below :

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