If refractive index of glass is 1.50 and of water is 1.33, then criticle angle is

Options

A. `sin^(-1)(8/9)`
B. `sin^(-1)(2/3)`
C. `cos^(-1)(8/9)`
D. None of the above

Explanation

To find the critical angle when light travels from glass to water, we can use the formula for the critical angle \( C \):

\[ C = \sin^{-1}\left(\frac{1}{\mu_{\text{relative}}}\right) \]

where \( \mu_{\text{relative}} \) is the relative refractive index of the two media.

### Step 1: Identify the refractive indices
We know:
- Refractive index of glass, \( \mu_{\text{glass}} = 1.50 \)
- Refractive index of water, \( \mu_{\text{water}} = 1.33 \)

### Step 2: Calculate the relative refractive index
The relative refractive index when light travels from glass to water is given by:

\[ \mu_{\text{relative}} = \frac{\mu_{\text{glass}}}{\mu_{\text{water}}} \]

Substituting the values:

\[ \mu_{\text{relative}} = \frac{1.50}{1.33} \]

### Step 3: Calculate the value of \( \mu_{\text{relative}} \)
Now, we perform the division:

\[ \mu_{\text{relative}} \approx 1.126 \]

### Step 4: Substitute into the critical angle formula
Now we substitute \( \mu_{\text{relative}} \) into the critical angle formula:

\[ C = \sin^{-1}\left(\frac{1}{\mu_{\text{relative}}}\right) = \sin^{-1}\left(\frac{1}{1.126}\right) \]

### Step 5: Calculate \( \frac{1}{\mu_{\text{relative}}} \)
Calculating \( \frac{1}{1.126} \):

\[ \frac{1}{1.126} \approx 0.887 \]

### Step 6: Find the critical angle
Now, we find the critical angle:

\[ C = \sin^{-1}(0.887) \]

Using a calculator, we find:

\[ C \approx 61.0^\circ \]

### Final Answer
Thus, the critical angle when light travels from glass to water is approximately \( 61.0^\circ \).

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