Snell’s Law (Grade 11 NSC Matric Physical Sciences): Revision Notes

Snell's Law

What is Snell's Law?

Snell's Law describes how light bends when it passes from one medium to another. This bending of light is called refraction. The law was discovered by Dutch physicist Willebrord Snell in 1621 and explains how to calculate the angle at which light will bend.

When light travels from one material (like air) into another material (like water or glass), it changes direction. The amount of bending depends on the refractive indices of both materials.

Definition and formula

Snell's Law states that:

$n_1 \sin \theta_1 = n_2 \sin \theta_2$

Where:

• $n_1$ = Refractive index of the first material
• $n_2$ = Refractive index of the second material
• $\theta_1$ = Angle of incidence (measured from the normal)
• $\theta_2$ = Angle of refraction (measured from the normal)

Understanding refraction direction

The direction light bends depends on the refractive indices of the two materials:

When light enters a denser medium (higher refractive index):

• Light bends towards the normal
• The angle of refraction is smaller than the angle of incidence
• Example: Light going from air into water or glass

When light enters a less dense medium (lower refractive index):

• Light bends away from the normal
• The angle of refraction is larger than the angle of incidence
• Example: Light going from water into air

Formal experiment 1: Verifying Snell's law

Aim:

To verify that Snell's Law is correct by measuring angles and calculating the relationship.

Apparatus:

• Glass block
• Ray box
• 360° protractor
• 5 pieces of A4 paper
• Pencil
• Ruler

Method:

1. Set up the apparatus: Place the glass block in the middle of an A4 paper. Draw around the block with a pencil to mark its outline.

2. Create light rays: Turn on the ray box and aim the light towards the glass block at different angles. Change the angle for each piece of paper.

3. Mark the light path: Draw dots to mark where the incoming light ray hits the surface and where the outgoing ray leaves the block.

4. Remove the block: Switch off the ray box and remove the glass block. Use a ruler to join the dots, creating straight lines that show the complete light path.

5. Measure the angles: Draw the normal (perpendicular line) to the surface where light enters the block. Use the protractor to measure $\theta_1$ and $\theta_2$.

6. Record data: Enter your measurements into a data table:

$\theta_1$	$\theta_2$	$n_1 \sin \theta_1$	$n_2 \sin \theta_2$

For this experiment:

• $n_1 = 1.0$ (air)
• $n_2 = 1.5$ (glass)

Results:

If Snell's Law is correct, the values in the last two columns should be equal ($n_1 \sin \theta_1 = n_2 \sin \theta_2$).

Formal experiment 2: Determining unknown refractive index

Aim:

To find the refractive index of an unknown transparent material using Snell's Law.

Apparatus:

• Ray box
• 360° protractor
• 5 pieces of A4 paper
• Block of unknown transparent material
• Pencil
• Ruler

Method:

Follow the same procedure as Experiment 1, but this time:

• $n_1 = 1.0$ (air - known)
• $n_2 = ?$ (unknown material)

Calculate $n_2$ using the rearranged formula: $n_2 = \frac{n_1 \sin \theta_1}{\sin \theta_2}$

$\theta_1$	$\theta_2$	$n_2 = \frac{n_1 \sin \theta_1}{\sin \theta_2}$

Discussion:

Take the average of your calculated $n_2$ values to get a good approximation of the unknown material's refractive index.

Special case: Normal incidence

When light hits a surface at 0° (along the normal), something interesting happens:

If $\theta_1 = 0°$, then $\sin \theta_1 = 0$

From Snell's Law: $n_1 \times 0 = n_2 \sin \theta_2$

Therefore: $\sin \theta_2 = 0$, so $\theta_2 = 0°$

Understanding refraction with analogies

Worked example 1: Finding an unknown refractive index

Worked example 2: Light from water to air

Worked example 3: Light from water to diamond

Key exam tips

Remember!