The angle of incidence for a ray light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are:

  • Option 1)

    45°; \frac{1}{\sqrt{2}}

  • Option 2)

    30°;\sqrt{2}

  • Option 3)

    45°;\sqrt{2}

  • Option 4)

    30°;\frac{1}{\sqrt{2}}

 

Answers (1)

As we learnt in

Condition of maximum deviation -

i=e

 

 

- wherein

delta _{min}= 2i-A

mu = frac{sin left ( frac{delta _{m}+A}{2} 
ight )}{sin left ( A/2 
ight )}

 

 

 

i =45

A=60

for minimum deviation

i =e=45^{\circ}

r_{1}=r_{2}=\frac{A}{2}

\delta _{min}=21-A

=90^{\circ}-60^{\circ}

=30^{\circ}

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

\mu\:=\:\frac{Sin(\frac{60+30}{2})}{Sin(\frac{A}{2})}\:=\:\frac{Sin45^{\circ}}{Sin30^{\circ}}

\mu\:=\sqrt{2}


Option 1)

45°; \frac{1}{\sqrt{2}}

Incorrect option

Option 2)

30°;\sqrt{2}

Correct option

Option 3)

45°;\sqrt{2}

Incorrect option

Option 4)

30°;\frac{1}{\sqrt{2}}

Incorrect option

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