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Question
A ray of light is incident on a prism whose refractive index is 1.52 at an angle of 40°. If the angle of emergence is 60°, calculate the angle of the prism.
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Solution
Given :
`mu = 1.52` `i = 40^circ`
`e = 60^circ` A = ?
`mu = sin i/sin r`
`1.52 = sin 40^circ/sin r`
`therefore sin r = 0.6427/1.52`
`sin r = 0.4228`
`therefore r = sin^-1(0.4228)`
`r = 25.01^circ`
`1/mu = (sin r')/sin e ⇒ sin r' = sin e/mu`
⇒ `sin r' = sin 60^circ/1.52 = 0.866/1.52 = 0.57`
⇒ `r' = sin^-1(0.57) = 34.75^circ`
`therefore A = r + r' = 25.01^circ + 34.75^circ = 59.76^circ`
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