The refractive index of air with respect to glass is expressed as `""_(g)mu_(a)=(sini)/(sinr)`.
(a) Write down a similar expression for `""_(a)mu_(g)` in terms of the angles `i` and r.
(b) if angle `r=90^@`, what is the corresponding angle `i` called ?
(c) What is the physical significance of the angle `i` in part (b) ?

Answer

Let's solve the question step by step.

### Step 1: Write down the expression for the refractive index of air with respect to glass.

The refractive index of air with respect to glass is given by:

\[ \mu_{g}^{a} = \frac{\sin i}{\sin r} \]

### Step 2: Write down a similar expression for \(\mu_{a}^{g}\).

To find the expression for \(\mu_{a}^{g}\), we take the inverse of the original equation. Thus, we have:

\[ \mu_{a}^{g} = \frac{\sin r}{\sin i} \]

### Step 3: Analyze the case when \(r = 90^\circ\).

If the angle of refraction \(r\) is \(90^\circ\), we can substitute this value into our expression for \(\mu_{a}^{g}\):

\[ \mu_{a}^{g} = \frac{\sin(90^\circ)}{\sin i} = \frac{1}{\sin i} \]

### Step 4: Identify the corresponding angle \(i\) when \(r = 90^\circ\).

When \(r = 90^\circ\), the angle \(i\) is referred to as the **critical angle**, denoted by \(i_c\).

### Step 5: Discuss the physical significance of the critical angle.

The physical significance of the critical angle \(i_c\) is that it marks the boundary between refraction and total internal reflection. When the angle of incidence \(i\) is greater than the critical angle \(i_c\), total internal reflection occurs, meaning that all the light is reflected back into the medium rather than being refracted.

### Summary of the Solution:

(a) The expression for \(\mu_{a}^{g}\) is:

\[ \mu_{a}^{g} = \frac{\sin r}{\sin i} \]

(b) The corresponding angle \(i\) when \(r = 90^\circ\) is called the **critical angle** \(i_c\).

(c) The physical significance of the critical angle \(i_c\) is that it is the angle of incidence above which total internal reflection occurs.

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