An equilateral glass prism has a refractive index 1.6 in air. calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index 4\sqrt{2}/5

 

 

 

 
 
 
 
 

Answers (1)

 

n=\frac{\sin \frac{\delta m +A}{2}}{\sin \frac{A}{2}}

Where, '\delta m' is the angle of minimum deviation,

  'n'  is the refractive index of the prism with respect to the medium 

 'A' is the angle of the prism 

Hence, 

The refractive index of the prism with respect to the medium will be - n=\frac{1.6}{\frac{4\sqrt{2}}{5}}=\frac{1.6}{4\sqrt{2}}\times \frac{5}{1}=\frac{8}{4\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}

 Now, substituting the above values, in the formula used:-

We have,

 \sqrt{2}=\frac{\sin (\frac{\delta m}{2}+\frac{60^{\circ}}{2})}{\sin \frac{60^{\circ}}{2}}=\frac{\sin \left ( \frac{\delta m}{2}+30^{\circ} \right )}{\sin 30^{\circ}} \frac{\sqrt{2}}{2}=\sin \left ( \frac{\delta m}{2}+30^{\circ} \right )            \left [ \because \sin 30^{\circ} =\frac{1}{2}\right ]

\frac{\delta m}{2}+30^{\circ}=sin^{-1}(\frac{1}{\sqrt{2}})

  \\\Rightarrow \frac{\delta m}{2}+30^{\circ}=45^{\circ}

  \delta m=30^{\circ}

Most Viewed Questions

Related Chapters

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions