Light is incident from glass medium to air medium- The variation of the angle of deviation - with the angle of incidence i for 0 - i - 90- is shown- The refractive index of glass is 2-3- If the value of x - y - z is n -6 then find value of n-

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Standard VII

Physics

Reflection

Light is inci...

Question

Light is incident from glass medium to air medium. The variation of the angle of deviation $δ$ with the angle of incidence $i$ for $0 < i < 90^{\circ}$ is shown. The refractive index of glass is $\frac{2}{\sqrt{3}}$ . If the value of $(x + y + z)$ is $\frac{n π}{6}$ then find value of n_______.

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Solution

From the figure, $x$ is the minimum angle of incidence for total internal reflection. $x = C = {sin}^{- 1} (\frac{\sqrt{3}}{2}) = \frac{π}{3}$ .

if , $i = C \to r = \frac{π}{2} \Rightarrow δ = (r - i) = \frac{π}{2} - C$

$\Rightarrow y = \frac{π}{2} - \frac{π}{3} . = \frac{π}{6}$ (for total internal reflection),

If $i = C \Rightarrow δ = 180^{\circ} - 2 i = 180 - 2 C . \Rightarrow z = π - 2 (\frac{π}{3}) = (\frac{π}{3})$

$x + y + z = \frac{π}{3} + \frac{π}{6} + \frac{π}{3} = \frac{5 π}{6}$

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Light is incident from glass medium to air medium. The variation of the angle of deviation δ with the angle of incidence i for 0<i<90∘ is shown. The refractive index of glass is 2√3. If the value of (x+y+z) is nπ6 then find value of n_______.

From the figure, x is the minimum angle of incidence for total internal reflection. x=C=sin−1(√32)=π3. if , i=C→r=π2⇒δ=(r−i)=π2−C ⇒y=π2−π3.=π6 (for total internal reflection), If i=C⇒δ=180∘−2i=180−2C.⇒z=π−2(π3)=(π3) x+y+z=π3+π6+π3=5π6

Light is incident from glass medium to air medium. The variation of the angle of deviation $δ$ with the angle of incidence $i$ for $0 < i < 90^{\circ}$ is shown. The refractive index of glass is $\frac{2}{\sqrt{3}}$ . If the value of $(x + y + z)$ is $\frac{n π}{6}$ then find value of n_______.