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A ray of light travels from air into a glass slab with a refractive index of 1.5. If the angle of incidence is 45 degrees, what is the sine of the angle of refraction?
0.47
0.52
0.61
0.75
0.47
To determine the sine of the angle of refraction, we apply Snell's Law, which relates the refractive indices and the sines of the angles of incidence and refraction. Given n1тАЛ=1.0 (air), n2тАЛ=1.5 (glass), and i=45┬░, we calculate sin(r)=1.5sin(45┬░)тАЛ.
To determine the sine of the angle of refraction, we apply Snell's Law, which relates the refractive indices and the sines of the angles of incidence and refraction. Given n1тАЛ=1.0 (air), n2тАЛ=1.5 (glass), and i=45┬░, we calculate sin(r)=1.5sin(45┬░)тАЛ.
Think of a car moving from a smooth pavement onto a muddy field at an angle; the wheel that hits the mud first slows down, causing the car to pivot or turn towards the normal line of the boundary.
n1тАЛsin(i)=n2тАЛsin(r) тАФ Snell's Law
sin(45┬░)тЙИ0.707 тАФ Trigonometric constant
Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, equal to the ratio of the refractive indices of the two media. When light enters an optically denser medium like glass from a rarer medium like air, it bends towards the normal, resulting in a smaller angle of refraction.
Light bends towards the normal when traveling from a rarer to a denser medium.
The refractive index is a unitless ratio comparing the speed of light in vacuum to the speed of light in the material.
Since the refractive index of glass is greater than air, the angle of refraction must be less than the angle of incidence.
Design of lenses for cameras and eyeglasses
Fiber optic communication systems
Calculation: sin(r)=1.50.707тАЛтЙИ0.471.
Option B (0.52), C (0.61), and D (0.75) are mathematically incorrect based on the application of Snell's Law.
A is correct тАФ The sine of the angle of refraction is calculated as 0.47 using the formula derived from Snell's Law.
Always remember the value sin(45┬░)=2тАЛ1тАЛтЙИ0.707; it is a frequently used constant in physics problems involving angles.
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