For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

  • Option 1)

    lies between 2 and \sqrt 2

  • Option 2)

    is less than 1

  • Option 3)

    is greater than 2

  • Option 4)

    lies between \sqrt 2 and 1

 

Answers (1)

\mu\:=\:\frac{Sin (\frac{A+\delta m}{2})}{Sin(\frac{A}{2})}.0

Here \delta _{m}\:=\:A\:\:\:\:\:\:\:\:\therefore\mu\:=\:\frac{Sin(\frac{A+A}{2})}{Sin(\frac{A}{2})}

\mu-2Cos\frac{A}{2}------1

In the given situation A can varies from 0 to 90.

\therefore\:\mu_{mim}-2.Cos(\frac{90}{2})-\sqrt{2}

\mu_{max}-2.Cos0^{\circ}=2

\therefore\:\mu lies between \sqrt{2} and 2.

 


Option 1)

lies between 2 and \sqrt 2

This option is correct.

Option 2)

is less than 1

This option is incorrect.

Option 3)

is greater than 2

This option is incorrect.

Option 4)

lies between \sqrt 2 and 1

This option is incorrect.

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