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  • A thin prism of angle and refractive index for yellow light <img alt="\left(\mathrm{n}_{\mathrm{Y}}\r

A thin prism of angle 6^{\circ} and refractive index for yellow light \left(\mathrm{n}_{\mathrm{Y}}\right) 1.5 is combined with another prism of angle 5^{\circ}$ and $\mathrm{n}_{\mathrm{Y}}=1.55. The combination produces no dispersion. The net average deviation (\delta) produced by the combination is \left(\frac{1}{x}\right)^{\circ}. The value of \mathrm{x} is_____________.

Option: 1

4


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Let the deviation through prism \mathrm{P_{1}} and prism \mathrm{P_{2}} be \mathrm{\delta _{1}} & \mathrm{\delta _{2}} respectively

\mathrm{\delta _{1}=A_{1}\left ( \mu _{1}-1 \right )}

      \mathrm{=6\degree\left ( 1.5-1 \right )}

\mathrm{\delta _{1}=3\degree}

\mathrm{\delta_2 =A_2\left(\mu_2-1\right) }

    \mathrm{=5^{\circ}(1.55-1) }

\mathrm{\delta _{2}=5^{\circ}(0.55) }

\mathrm{\delta _{1}\: and\: \delta _{2}} are in opposite direction

\mathrm{\delta_1+\delta_2 =3^{\circ}+\left(-5^{\circ}(0.55)\right) }

\mathrm{\delta_1+\delta_2 =(0.25)^{\circ} }

\mathrm{\text { Net average deviation } ={\delta_1+\delta_2}}

                                              \mathrm{={-(0.25)^{\circ}}}

                                              =\frac{1}{4}

\mathrm{\therefore x =4}

Posted by

Ritika Harsh

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