Question

sini
μ =
sinr
Find r if u = 1.5 and i = 60°​

Answer 1

Solution :

This is a simple application of the snell's law . We need to find the value of r here .

Acc to the snell's law :

(Sin i)/(sin r) = μ1/μ2

> [ sin 60 ]/[ sin r] = 1.5/μ2

> √3/2 × (1/sinr) = 3/2 × 1/(μ2)

> √3/(sinr) = 3/μ2

> sin r = √3 μ2/3

> sin r = ( 1/√3) μ2

> r = sin^-1 [ μ2/√3 ] .

This is the required answer .

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Additional Information :

The refractive index of some common mediums are -

$\begin{array}{|c|c|} \cline {1-2}\bf Object & \bf {Refractive\:Index} \\\dfrac{\qquad\qquad\qquad\qquad}{}&\dfrac{\qquad\qquad\qquad\qquad}{} \\\sf Air & \sf 1.0003 \\ &\\\sf Ice & 1.31 \\ & \\ \sf Water & 1.33 \\&\\ \sf Alcohol & 1.36 \\&\\ \sf Kerosene & 1.44 \\&\\ \sf Liquefied\: Quartz & 1.46 \\&\\ \sf Torpene-Tyne\:oil & 1.47 \\&\\ \sf Benzene & 1.50 \\&\\ \sf Crown\:Glass & 1.52 \\&\\ \sf Canada\:Balsum & 1.53 \\&\\ \sf Rock\:Salt & 1.54 \\&\\ \sf Carbon\:Di sulphate & 1.63 \\&\\ \sf Dark\:Flint\:Glass & 1.65 \\&\\ \sf Ruby & 1.71 \\&\\ \sf Diamond & 2.42 \\ \cline {1-2}\end{array}$

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Answer 2

Solution :

This is a simple application of the snell's law . We need to find the value of r here .

Acc to the snell's law :

(Sin i)/(sin r) = μ1/μ2

> [ sin 60 ]/[ sin r] = 1.5/μ2

> √3/2 × (1/sinr) = 3/2 × 1/(μ2)

> √3/(sinr) = 3/μ2

> sin r = √3 μ2/3

> sin r = ( 1/√3) μ2

> r = sin^-1 [ μ2/√3 ] .

This is the required answer .

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↪️ llMichhChocoll