1. Use the formula for critical angle

For light going from a denser medium to a rarer medium, the critical angle $C$ satisfies:

$\sin C = \frac{n_2}{n_1}$

where:

• $n_1$ = refractive index of first medium (denser)
• $n_2$ = refractive index of second medium (rarer)

2. Given critical angle

$C = 45^\circ$

So,

$\sin 45^\circ = \frac{n_2}{n_1}$

$\frac{1}{\sqrt{2}} = \frac{n_2}{n_1}$

3. Find the ratio

Rearranging,

$\frac{n_1}{n_2} = \sqrt{2}$

Hence,

$n_1 : n_2 = \sqrt{2} : 1$

4. Match with the options

This corresponds to:

D: $\sqrt{2} : 1$

5. Verification with stored answer

Stored correct answer = D

Our derived answer = D

So, they agree.