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Calculating the Angle of Refraction: A Comprehensive Guide

April 07, 2025Technology1353
Calculating the Angle of Refraction: A Comprehensive Guide To understa

Calculating the Angle of Refraction: A Comprehensive Guide

To understand the angle of refraction when a ray of light strikes a glass slab at a specific angle, we can use Snell's Law, a fundamental concept in optics. This law is crucial for understanding the behavior of light as it passes from one medium to another.

Understanding Snell's Law

Snell's Law is given by the formula:

n_1 sintheta_1 n_2 sintheta_2

where:

n_1 is the refractive index of the first medium (air, which is approximately 1.00) theta_1 is the angle of incidence n_2 is the refractive index of the second medium (glass, typically ranging from about 1.5 to 1.9) theta_2 is the angle of refraction

Step-by-Step Calculation

To find the angle of refraction when a ray of light strikes a glass slab at 30°, we need to follow these steps:

Identify the Indices

In this case, we use the refractive indices:

n- n_1 for air 1.00 n- n_2 for glass 1.5 theta_1 30° (the angle of incidence)

Substitute these values into Snell's Law:

1.00 cdot sin30^circ 1.5 cdot sintheta_2

Step 2: Calculate (sin30°)

sin30^circ 0.5

Substitute this value into the equation:

1.00 cdot 0.5 1.5 cdot sintheta_2

Step 3: Solve for (sintheta_2)

0.5 1.5 cdot sintheta_2

sintheta_2 frac{0.5}{1.5} frac{1}{3} approx 0.3333

Step 4: Calculate (theta_2)

Using the inverse sine function:

theta_2 sin^{-1}(0.3333) approx 19.47^circ

Conclusion

The angle of refraction when the ray of light strikes the glass slab at 30° is approximately 19.47°.

Additional Examples

Let's extend this understanding to different scenarios:

Borosilicate Crown Glass

For Borosilicate Crown Glass with a refractive index of 1.51124 at 589nm yellow light:

theta_2 sin^{-1}frac{sin30^circ}{1.51124} approx 19.32^circ

A rough check can use the simpler values: sin30° 1/2 and Crown glass n ≈ 3/2, giving an angle of refraction of approximately 19.47°.

Perspex (Acrylic)

For light passing through Perspex (with a refractive index of 1.495), we calculate:

sintheta_2 frac{sin30^circ}{1.495} frac{1/2}{1.495} approx 0.3344

theta_2 sin^{-1}(0.3344) approx 19.54^circ

When the light exits the Perspex sheet back into air, the angle of refraction is the same as the angle of incidence due to the principle of reversibility of light paths.