The velocities of light in air and glass are 3.0 x10\(^8\)ms\(^{-1}\) and 1.8 \(\times \)10\(^8\) ms\(^{-1}\) respectively. Calculate the sine of the angle of incidence that will produce an angle of refraction of 30^\circ for a ray of light incident on glass.
A
1.2
B
1.0
C
0.8
D
0.6
E
0.3
Verified Correct Answer: C.
Physical Principles & Numerical Solution
\(n_1 \sin(\theta_1)\) = \(n_2 \sin(\theta_2\)
BUT, n = \(\frac{c}{v}\), where c is the speed of light in vacuum (approximately equal to the speed of light in air) and v is the speed of light in the medium.
For air, n\(_1\) = \(\frac{3 \times 10^8}{3 \times 10^8}\) = 1
For glass, n\(_2\) = \(\frac{3 \times 10^8}{1.8 \times 10^8}\) ≈ 1.667
Applying snell's law: \(n_1 \sin(\theta_1)\) = \(n_2 \sin(\theta_2)\) = \(1 \sin(\theta_1)\) = 1.667 sin(30) = 0.83335
Thus, the sine of the angle of incidence is ≈ 0.8
Source: Myschool Past Questions Archive (Record #21240)