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Manipal Engineering Manipal Engineering Solved Paper-2015

  • question_answer
    Figure shows an irregular block of material of refractive index \[f(x)=\left\{ \begin{matrix}   \frac{\sin (\cos x)-\cos x}{{{(\pi -2x)}^{3}}}, & x\ne \frac{\pi }{2}  \\   k, & x=\frac{\pi }{2}  \\ \end{matrix} \right.\]A ray of light strikes the face AB as shown in figure. After refraction, it is incident on a spherical surface CD of radius of curvature 0.4 m and enters a medium of refractive index 1.514 to meet PQ at E. Find the distance OE up to two places of decimal.

    A)  7m                        

    B) 7.29m 

    C) 6.06 m                                  

    D)  8.55 m

    Correct Answer: C

    Solution :

    (c) From Snell's law, \[6.60\times {{10}^{-23}}g\] \[3.30\times {{10}^{-23}}g\]\[2.20\times {{10}^{-23}}g\] \[13.20\times {{10}^{-23}}g\]\[({{m}_{p}}=1.6\times {{10}^{-27}}kg)\] This means that the ray becomes parallel to side AD inside the slab. This implies for the second face \[{{10}^{20}}kg/{{m}^{3}}\] Given        R = 0.4 m \[{{10}^{17}}kg/{{m}^{3}}\] \[{{10}^{14}}kg/{{m}^{3}}\]\[{{10}^{11}}kg/{{m}^{3}}\] \[\alpha ={{\tan }^{-1}}\left( \frac{1}{5} \right).\] \[a=2m{{s}^{-2}}.\]upto 2 decimal places)


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