WAEC - Physics (1988 - No. 25)

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° for a ray of light incident on glass.
1.2
1.0
0.8
0.6
0.3

Explanation

\(n_1 \sin(\theta_1)\)  = \(n_2 \sin(\theta_2\)

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

 

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