Maud measures one crossing precisely. A ray passes from air (n = 1.00) into water (n = 1.33). It arrives at 45.0° from the normal and continues at 32.0° from the normal.
Toward or away ranks bends in words. This lesson states the exact law that ties the two angles together.
Try one combination of Maud's numbers. Take each side's index, and multiply it by the sine of that side's angle.
Air side: 1.00 × sin 45.0°, and sin 45.0° = 0.71, so the product is 1.00 × 0.71 = 0.71.
Water side: 1.33 × sin 32.0°, and sin 32.0° = 0.53, so the product is 1.33 × 0.53 = 0.70.
The two products match, within the rounding of the measurement. That match is not luck: it holds at every boundary.
This is called Snell's law. Side 1 is where the light starts; side 2 is where it goes. The subscripts just name the two sides of the boundary.
Both angles are measured from the normal, never from the surface. The sine here is the same sine ratio you used in the math-tools topic: a number your calculator gives for any angle.
Snell's law contains the toward/away rule. If side 2's index is larger, then sin θ₂ must be smaller to keep the products equal, so θ₂ is smaller: the ray lies closer to the normal, exactly as the denser-means-toward rule said.
A ray passes from air (n = 1.00) into a glass block (n = 1.50), arriving at 60.0° from the normal and continuing at 35.3° from the normal. Show that these measurements obey Snell's law.
Write down the values:
n₁ = 1.00, θ₁ = 60.0°, n₂ = 1.50, θ₂ = 35.3°
Write down the equation:
n₁ sin θ₁ = n₂ sin θ₂
Substitute in the values, and calculate each side:
Side 1: sin 60.0° = 0.87, and 1.00 × 0.87 = 0.87. Side 2: sin 35.3° = 0.58, and 1.50 × 0.58 = 0.87.
The two sides give the same product, 0.87, so the measurements obey Snell's law.
Light passes from water (n = 1.33) into a diamond (n = 2.42). Name each quantity in n₁ sin θ₁ = n₂ sin θ₂ for this crossing.
Side 1 is where the light starts: the water. So n₁ = 1.33, and θ₁ is the angle in the water, measured from the normal.
Side 2 is where the light goes: the diamond. So n₂ = 2.42, and θ₂ is the angle in the diamond, measured from the normal.
No number is computed here: the law only names how the four quantities sit.
n₁ = 1.33 with θ₁ in the water; n₂ = 2.42 with θ₂ in the diamond; both angles from the normal.
At one boundary crossing, which two products does Snell's law set equal?
Snell's law uses an angle on each side of the boundary. Each angle is measured between the ray and which line?
Oona says: 'If the two media on either side of a boundary were identical, Snell's law would force the two angles to be equal, so the ray would go straight through.' Is Oona correct?
Which statement about Snell's law is true?
Light passes from glycerin (n = 1.47) into air (n = 1.00). In n₁ sin θ₁ = n₂ sin θ₂, which value plays the part of n₁?
Light passes from water (n = 1.33) into sapphire (n = 1.77). Without calculating, compare the sines of the two angles. The sine of the angle in the sapphire is: