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Physics-

General

Easy

Question

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $mu$ , a rav, incident at an angle $theta$ , on the face AB would get transmitted through the face AC of the prism provided :

$θ > {c o s}^{- 1} [μ s i n (A + {s i n}^{- 1} (\frac{1}{μ}))]$
$θ < {c o s}^{- 1} [μ s i n (A + {s i n}^{- 1} (\frac{1}{μ}))]$
$θ > {s i n}^{- 1} [μ s i n (A - {s i n}^{- 1} (\frac{1}{μ}))]$
$θ > {s i n}^{- 1} [μ s i n (A - {s i n}^{- 1} (\frac{1}{μ}))]$

The correct answer is: $theta greater than s i n to the power of negative 1 end exponent invisible function application open square brackets mu s i n invisible function application open parentheses A minus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses close parentheses close square brackets$

$table row cell r subscript 2 end subscript less than theta subscript c end subscript end cell row cell r subscript 2 end subscript less than s i n to the power of negative 1 end exponent invisible function application left parenthesis 1 divided by mu right parenthesis end cell row cell s i n invisible function application r subscript 2 end subscript less than 1 divided by mu end cell row cell s i n invisible function application theta equals mu s i n invisible function application r subscript 1 end subscript end cell row cell r subscript 1 end subscript equals s i n to the power of negative 1 end exponent invisible function application left parenthesis s i n invisible function application theta divided by mu right parenthesis end cell row cell s i n invisible function application open parentheses A minus r subscript 1 end subscript close parentheses less than 1 divided by mu end cell end table$
$table row cell s i n invisible function application open parentheses A minus open parentheses sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator sin invisible function application theta over denominator mu end fraction close parentheses close parentheses close parentheses less than fraction numerator 1 over denominator mu end fraction end cell row cell A minus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator sin invisible function application theta over denominator mu end fraction close parentheses less than s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses end cell row cell A minus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses less than s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator sin invisible function application theta over denominator mu end fraction close parentheses end cell row cell open square brackets sin invisible function application open parentheses A minus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator m end fraction close parentheses close parentheses close square brackets less than fraction numerator sin invisible function application theta over denominator mu end fraction end cell row cell s i n to the power of negative 1 end exponent invisible function application open square brackets mu open square brackets sin invisible function application open parentheses A minus s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator m end fraction close parentheses close parentheses close square brackets less than theta close end cell end table$

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