SPM Physics: AHA! Refractive Index – One Quantity, Four Styles!

 

Refractive index, n, is one of the most versatile quantities in optics. In SPM, it can appear in four different question styles:

1️⃣ Speed of light in medium

$$n=\frac{c}{v}$$

Higher n→ lower v. Optically denser medium slows light down.

2️⃣ Snell’s Law (Refraction)

$$n=\frac{\sin i}{\sin r}$$

For air → glass,

$i>r$

Light bends towards the normal.

3️⃣ Critical angle

$$n=\frac{1}{\sin c}$$

Smaller critical angle → larger refractive index. Key for total internal reflection.

4️⃣ Real depth vs Apparent depth

$$n=\frac{H}{h},h=\frac{H}{n}$$

Objects under water appear shallower. Apparent depth is always less than real depth.

Exam tip:

• Always draw the normal line.

• Don’t confuse apparent depth ÷ real depth (wrong).

• Remember: higher refractive index = slower speed, smaller critical angle.

AHA! One refractive index, four exam styles. Not by sight, but by INSIGHT!

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