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| 1. |
Define Snell's Law. Using a neat labelled diagram derive an expression for the refractive index of the material of an equilateral prism. |
| Answer» <html><body><p></p>Solution :Snell's law : <br/> The ratio of the sine of the <a href="https://interviewquestions.tuteehub.com/tag/angle-875388" style="font-weight:bold;" target="_blank" title="Click to know more about ANGLE">ANGLE</a> of incidence to the sine of angle of refraction is constant, called the refractive index of the medium. <br/> `(sini)/(sinr)=mu"(constant)".` <br/> Let ABC be the glass prism. Its angle of prism is A. The refractive index of the material of the prism is `mu`. Let AB and AC be the two refracting surfaces PQ = incident ray, RS = <a href="https://interviewquestions.tuteehub.com/tag/emergent-2610413" style="font-weight:bold;" target="_blank" title="Click to know more about EMERGENT">EMERGENT</a> ray. <br/> `"Let angle of incidence "= r_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)"angle of emergence "=i_(2)` <br/> `"angle of refraction "=r_(1)"angle of refraction at R"=r_(2)` <br/> After travelling through the prism it falls on AC and emerges as RS. <br/> The D = angle of deviation. <br/> From the `DeltaQRT` <br/> `r_(1)+r_(2)+angleT=<a href="https://interviewquestions.tuteehub.com/tag/180-279527" style="font-weight:bold;" target="_blank" title="Click to know more about 180">180</a>^(@)"..................(1)"` <br/> From the quadrilateral AQTR <br/> `angleA+angleT=180^(@)` <br/> `angleT=180^(@)-A."..............(2)"` <br/> From the equations (1) and (2) <br/> `r_(1)+r_(2)+angleT=180^(@)" we get "` <br/> `r_(1)+r_(2)+180^(@)-A=180^(@)` <br/> `r_(1)+r_(2)=A."...............(3)"` <br/> from the `DeltaQUR` <br/> `i_(1)-r_(1)+i_(2)-r_(2)+180^(@)-D=180^(@)` <br/> `i_(1)+i_(2)-(r_(1)+r_(2))=D` <br/> `i_(1)+i_(2)-A=D""[because r_(1)+r_(2)=A]` <br/> `i_(1)+i_(2)=A+D"....................(4)"`<br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/VIK_PHY_QB_C02_E03_008_S01.png" width="80%"/> <br/> <a href="https://interviewquestions.tuteehub.com/tag/minimum-561095" style="font-weight:bold;" target="_blank" title="Click to know more about MINIMUM">MINIMUM</a> deviation : Experimentally it is found that as the angle of incidence increased the angle of deviation decreases till it reaches a minimum value and then it increases. This least value of deviation is called angle of minimum deviation `'delta'` as shown in the fig. <br/> When D decreases the two angles `i_(1) and i_(2)` become closer to each other at the angle of minimum deviation, the two angles of incidence are same i.e., `i_(1)=i_(2)` <br/> As `i_(1)=i_(2), r_(1)=r_(2)` <br/> `therefore i_(1)=i_(2)=i, r_(1)=r_(2)=r,` <br/> substituting this in (1) and (2) we get<br/> `"2r = A"rArr r=A//2` <br/> `i+i=A+delta rArr i=(A+delta)/(2)` <br/> According to Snell's law `mu=("Sin i")/("Sin r")` <br/> `mu=("sin"((A+delta)/(2)))/("Sin A/2")` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/VIK_PHY_QB_C02_E03_008_S02.png" width="80%"/></body></html> | |