A thin prism of angle 6 ° and refractive index for yellow light n Y 1 . 5 is combined with another prism of angle 5 ° and n Y = 1 . 55 . The combination produces no dispersion. The net average deviati

Question

A thin prism of angle 6 ° and refractive index for yellow light n Y 1 . 5 is combined with another prism of angle 5 ° and n Y = 1 . 55 . The combination produces no dispersion. The net average deviation δ produced by the combination is 1 x ° . The value of x is _____ .

TestHub · Accepted Answer

The formula for deviation due to a thin prism is given by, $δ = A (μ - 1)$ .
Therefore, for prism $1$ :
$δ_{1} = 6 (1.5 - 1) = 3 °$
And for prism $2$ :
$δ_{2} = - 5 (1.55 - 1) = - 2.75 °$
$\Rightarrow δ_{net} = δ_{1} + δ_{2} = 3 ° - 2.75 ° = 0.25 ° = {(\frac{1}{4})}^{°}$
Therefore, $x = 4$ .

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