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Snell's Law Calculator

Calculate refraction angles, critical angles, and refractive indices using Snell's law with interactive visualization

Parameters

°ⓘ
Angle of incident light ray
ⓘ
Refractive index of first medium
ⓘ
Refractive index of second medium
nmⓘ
Wavelength of light (for dispersion)
Show Trail

Controls

xⓘ

Calculated Values

Refracted Angle:
19.47;°19.47;°
Critical Angle:
NaN;°NaN;°
Total Internal Reflection:
0.00;0.00;
Speed Ratio:
1.50;1.50;

Examples

Example 1: Air to Glass

Light passing from air (n=1) to glass (n=1.5) at 30° incident angle.

  • Refracted Angle: 19.4719.47
  • Critical Angle: 41.8141.81
  • Total Internal Reflection: 0.000.00
  • Speed Ratio: 0.670.67

Example 2: Glass to Air

Light passing from glass (n=1.5) to air (n=1) at 45° incident angle.

  • Refracted Angle: 77.1077.10
  • Critical Angle: 41.8141.81
  • Total Internal Reflection: 0.000.00
  • Speed Ratio: 1.501.50

Example 3: Total Internal Reflection

Light in glass (n=1.5) hitting air (n=1) at 50° incident angle.

  • Refracted Angle: 0.000.00
  • Critical Angle: 41.8141.81
  • Total Internal Reflection: 1.001.00
  • Speed Ratio: 1.501.50

Visualization

Snell's Law and Optical Refraction

Snell's law describes how light bends when it passes from one medium to another with different refractive indices. The law states that n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the incident and refracted angles.

The refractive index (n) of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium: n = c/v. Higher refractive index means slower light speed and greater bending.

When light passes from a medium with higher refractive index to one with lower refractive index, there exists a critical angle beyond which total internal reflection occurs. The critical angle is given by θc = arcsin(n₂/n₁).

The relationship between incident and refracted angles depends on the refractive indices. If n₁ < n₂, light bends toward the normal (θ₂ < θ₁). If n₁ > n₂, light bends away from the normal (θ₂ > θ₁).

Refraction is responsible for many optical phenomena including the bending of light in lenses, the formation of rainbows, and the apparent position of objects underwater.

Key Concepts

  • Snell's Law: n₁sin(θ₁) = n₂sin(θ₂) (fundamental refraction law)
  • Refractive Index: n = c/v (ratio of light speeds)
  • Critical Angle: θc = arcsin(n₂/n₁) (total internal reflection)
  • Speed Ratio: v₂/v₁ = n₁/n₂ (speed relationship)
  • Wavelength Ratio: λ₂/λ₁ = n₁/n₂ (wavelength relationship)
  • Total Internal Reflection: Occurs when θ₁ > θc

Real-World Applications

  • Lens Design: Eyeglasses, cameras, and microscopes
  • Fiber Optics: Light transmission in optical fibers
  • Prisms: Light dispersion and spectrum analysis
  • Underwater Vision: Correction for apparent object positions
  • Rainbow Formation: Atmospheric refraction and reflection

Explore Further

More optics tools

Physics Equations

Snell's Law:
n1sin⁡(θ1)=n2sin⁡(θ2)n_1\sin(\theta_1) = n_2\sin(\theta_2)
Critical Angle:
θc=arcsin⁡(n2n1)\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)
Refractive Index:
n=cvn = \frac{c}{v}
Speed Ratio:
v2v1=n1n2\frac{v_2}{v_1} = \frac{n_1}{n_2}
Wavelength Ratio:
λ2λ1=n1n2\frac{\lambda_2}{\lambda_1} = \frac{n_1}{n_2}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Convert to Radians

Convert incident angle to radians:

Equation:

θ1=θ1°×π180°\theta_1 = \theta_1° \times \frac{\pi}{180°}

Calculation:

θ1=30°×π180°=0.524 rad\theta_1 = 30° \times \frac{\pi}{180°} = 0.524 \text{ rad}

Explanation:

Trigonometric functions in calculators use radians.

2

Step 2: Apply Snell's Law

Use Snell's law to find sin(θ₂):

Equation:

n1sin⁡(θ1)=n2sin⁡(θ2)n_1\sin(\theta_1) = n_2\sin(\theta_2)

Calculation:

sin⁡(θ2)=n1sin⁡(θ1)n2=1×sin⁡(0.524)1.5=0.333\sin(\theta_2) = \frac{n_1\sin(\theta_1)}{n_2} = \frac{1 \times \sin(0.524)}{1.5} = 0.333

Explanation:

This gives the sine of the refracted angle.

3

Step 3: Calculate Refracted Angle

Find the refracted angle:

Equation:

θ2=arcsin⁡(sin⁡(θ2))\theta_2 = \arcsin(\sin(\theta_2))

Calculation:

θ2=arcsin⁡(0.333)=19.47°\theta_2 = \arcsin(0.333) = 19.47°

Explanation:

Convert back to degrees for the final answer.

4

Step 4: Calculate Critical Angle

Find the critical angle:

Equation:

θc=arcsin⁡(n2n1)\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)

Calculation:

θc=arcsin⁡(1.51)=NaN°\theta_c = \arcsin\left(\frac{1.5}{1}\right) = NaN°

Explanation:

Critical angle exists only when n₁ > n₂.

5

Step 5: Check for Total Internal Reflection

Determine if total internal reflection occurs:

Equation:

Total Internal Reflection=θ1>θc\text{Total Internal Reflection} = \theta_1 > \theta_c

Calculation:

30°<NaN°⇒No30° < NaN° \Rightarrow No

Explanation:

Total internal reflection occurs when incident angle exceeds critical angle.

Frequently Asked Questions (FAQ)

What is Snell's law?

Snell's law states that n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are refractive indices and θ₁ and θ₂ are incident and refracted angles. It describes how light bends when passing between different media.

How do I calculate the refracted angle?

Use Snell's law: θ₂ = arcsin((n₁sin(θ₁))/n₂). The refracted angle depends on the incident angle and the ratio of refractive indices.

What is the critical angle?

The critical angle is the incident angle at which total internal reflection begins. It's calculated as θc = arcsin(n₂/n₁) when n₁ > n₂.

When does total internal reflection occur?

Total internal reflection occurs when light passes from a higher refractive index medium to a lower one, and the incident angle exceeds the critical angle.

How does refractive index affect light speed?

Higher refractive index means slower light speed in that medium. The relationship is n = c/v, where c is speed in vacuum and v is speed in the medium.

What is the relationship between wavelength and refractive index?

Wavelength changes when light passes between media: λ₂/λ₁ = n₁/n₂. Higher refractive index means shorter wavelength in that medium.

Practice MCQs

  1. Snell's law relates:
  2. When n₁ > n₂, light bends:
  3. Critical angle exists when:
  4. Higher refractive index means:
  5. Total internal reflection occurs when:

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