Question

A. State Snell's Law of refraction.
B. Define the refractive index of a material with respect to another material giving the mathematical expression.

Hint:

Snell's law relates the sines of the two angles. The refractive index compares the speeds of light in the two media.

Answer 1

Step 1: Part A: Snell's law of refraction:
When light goes from one medium to another, it bends at the surface. Snell's law gives the rule for this bending. It says that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for light of a given colour and for a given pair of media.

Step 2: Write the law as an expression:
If \(i\) is the angle of incidence and \(r\) is the angle of refraction, then
\[ \frac{\sin i}{\sin r} = \text{constant} \]

Step 3: Part B: Refractive index:
Take a ray going from medium 1 to medium 2. Let \(v_1\) be the speed of light in medium 1 and \(v_2\) the speed of light in medium 2. The refractive index of medium 2 with respect to medium 1 is the ratio of the speed of light in medium 1 to its speed in medium 2.

Step 4: Write the expression:
\[ n_{21} = \frac{v_1}{v_2} = \frac{\sin i}{\sin r} \]
The constant in Snell's law is this refractive index. It has no unit because it is a ratio of two speeds.

Final Answer:
Snell's law: \(\dfrac{\sin i}{\sin r}\) is constant for a given pair of media and a given colour of light. Refractive index: \(n_{21} = \dfrac{v_1}{v_2}\). \[ \boxed{\dfrac{\sin i}{\sin r} = \text{constant}, \quad n_{21} = \dfrac{v_1}{v_2}} \]