1. Why we need Snell’s law
When light travels from one transparent medium to another, it bends because its speed changes. I already know the basic rule: towards the normal when entering a denser medium, and away from the normal when entering a rarer medium. But to find exactly how much the ray bends, I need a mathematical rule. That rule is Snell’s law.
Snell’s law helps me calculate the refracted angle when I know the refractive indices and the angle of incidence. It turns the bending of light into a simple geometry–math problem.
2. The statement of Snell’s law
Snell’s law gives a fixed relationship between the angle at which the ray enters and the angle at which it bends in the second medium. It is written as:
\( n_1 \sin i = n_2 \sin r \)
Here:
- \( n_1 \) = refractive index of the first medium
- \( n_2 \) = refractive index of the second medium
- \( i \) = angle of incidence
- \( r \) = angle of refraction
This equation works beautifully for all transparent media.
3. Understanding the terms in Snell’s law
To apply the formula correctly, I remind myself what each angle and refractive index means:
- Angle of incidence (i): Measured between the incident ray and the normal.
- Angle of refraction (r): Measured between the refracted ray and the normal.
- Refractive index (n): Tells how much light slows inside that medium.
If the ray enters a medium with higher refractive index, \( r \) becomes smaller than \( i \). If it enters a medium with lower refractive index, \( r \) is larger than \( i \).
4. Ratio form of Snell’s law
Another way to write Snell’s law is:
\( \dfrac{\sin i}{\sin r} = \dfrac{n_2}{n_1} \)
This shows that the ratio of the sines of the angles depends only on how fast light moves in the two media.
5. Speed form of Snell’s law
Since refractive index is related to speed by \( n = \dfrac{c}{v} \), Snell’s law can also be written as:
\( \dfrac{\sin i}{\sin r} = \dfrac{v_1}{v_2} \)
This version reminds me that bending happens because the speed of light changes across the boundary.
6. How Snell’s law explains bending direction
Snell’s law automatically tells me whether the ray bends toward or away from the normal:
- If \( n_2 > n_1 \), then \( r < i \) → ray bends toward the normal.
- If \( n_2 < n_1 \), then \( r > i \) → ray bends away from the normal.
So I can predict the bending even before doing any calculations.
7. A simple example using numbers
Suppose a ray moves from air into glass. Let:
- \( n_1 = 1.00 \)
- \( n_2 = 1.50 \)
- \( i = 30^\circ \)
Using Snell’s law:
\( 1.00 \sin 30^\circ = 1.50 \sin r \)
\( 0.5 = 1.50 \sin r \)
\( \sin r = \dfrac{0.5}{1.50} = 0.333... \)
So:
\( r \approx 19.5^\circ \)
The refracted angle is smaller than the incident angle, so the ray bends toward the normal — matching the rule for entering a denser medium.
8. Where Snell’s law shows up in daily life
Once I know Snell’s law, many familiar things make sense:
- A straw in a glass of water looking bent.
- A coin under water appearing raised up.
- Light focusing inside lenses.
- Prisms bending and splitting white light.
Even though these effects look different, they all follow the same Snell’s-law bending rule.