Answer:
i = 61 degree
Explanation:
Given,
[tex]\alpha =45^{o}[/tex]
Now, by the snell's law
[tex]sin\theta_c=\frac{1}{n}\\sin\theta_c=\frac{1}{2.450}\\\theta_c=24.09^o[/tex]
Now,
Sin i / sin r = n 2 / n 1
sin i / sin r (45 - 24.09) = 2.45 / 1
i = 60.97 degree
The largest possible value of the incident angle to undergo the total internal reflection is [tex]61.04^{\circ}[/tex].
Given data:
The angle between the top surface and bottom surface of diamond is, [tex]\alpha=45^ {\circ}[/tex].
The given problem will utilize the Snell's law for the solution. As per the Snell's law , the ratio of sine of angle of incidence and sine of angle of refraction is equal to the ratio of refracted index and incident index.
As per the Snell' s law,
[tex]\dfrac{sini}{sinr} =\dfrac{n'}{n}[/tex] ..........................................................................(1)
n' is the refractive index of diamond. (n' =2.45)
n is the refractive index of air. (n = 1)
Here, r is the refracted angle and its value is, [tex]r = \alpha - \theta_{c}[/tex].
[tex]\theta_{c}[/tex] is critical angle and its value is calculated as,
[tex]sin\theta_{c}=\dfrac{1}{n'} \\\\sin\theta_{c}=\dfrac{1}{2.450} \\\\\theta_{c} = sin^{-1}(0.408)\\\\\theta_{c} = 24.07^{\circ}[/tex]
Substitute the values in equation (1) as,
[tex]\dfrac{sini}{sin( \alpha - \theta_{c})} =\dfrac{2.45}{1}\\\\\dfrac{sini}{sin( 45 - 24.07)} =\dfrac{2.45}{1}\\\\sini =2.45 \times sin(20.93)\\\\i = sin^{-1}(0.875)\\\\i = 61.04^{\circ}[/tex]
Thus, the required largest possible value of the incident angle to undergo the total internal reflection is [tex]61.04^{\circ}[/tex].
Learn more about the Snell's law here:
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