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Two parallel beams of light \( P \& Q \) (separation d) containing radiations of wavelengths \( 4000 A \) \& \( 5000 \AA \) (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure. The refractive index of the prism as a function of wavelength is given by the relation, \( \mu(\lambda)=1.20+\frac{b}{\lambda^{2}} \), where \( \lambda \) is in \( A \& b \) is a positive constant. The value of \( b \) is such that the condition for total reflection at the face \( A C \) is just satisfied for one wavelength \( \& \) is not satisfied for the other. A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper \& the lower beams immediately after transmission from the face AC, are \( 4 \mathrm{I} \& \mathrm{I} \) respectively, find the resultant intensity at the focus.
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