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Please help! A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracti

A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be :

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

    10°

 
Answers (1)
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As we learnt in

Condition for deviation without dispersion -

\left ( \mu _{v}-\mu _{r} \right )A+\left ( \mu{}'_{v}-\m{}'u _{r} \right )A{}'= 0

- wherein

\mu _{v} = Refractive index of violet ( prism 1)

\mu _{r}= Refractive index of red ( prism 1)

\mu{}' _{v} = Refractive index of violet ( prism 2)

\mu{}' _{r}= Refractive index of red ( prism 2)

 

 

 

For dispersion without deviation \\ \left | S_{1} \right |=\left | S_{2} \right |\\ (\mu_{1-1} )A_{1}=(\mu _{2}-1).A_{2}\\ or (1.42-1)\times 10=(1.7-1)(A_{2})\\ or A_{2}=\frac{0.42\times 10}{0.7}=6^{o}


Option 1)

This option is incorrect 

Option 2)

This option is correct 

Option 3)

This option is incorrect 

Option 4)

10°

This option is incorrect 

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