An object is seen through a glass slab of thickness `36 cm` and refractive index `3//2.` The observer, and the slab are dipped in water `(mu=4//3).` The shift produced in the position of the object is

Options

A. `12 cm`
B. `4 cm`
C. `6 cm`
D. `8 cm`

Explanation

To find the shift produced in the position of the object when viewed through a glass slab submerged in water, we can use the formula for the shift due to refraction:

\[ \text{Shift} (\Delta x) = t \left(1 - \frac{\mu_{\text{water}}}{\mu_{\text{slab}}}\right) \]

Where:
- \( t \) = thickness of the slab
- \( \mu_{\text{water}} \) = refractive index of water
- \( \mu_{\text{slab}} \) = refractive index of the glass slab

### Step 1: Identify the given values
- Thickness of the glass slab, \( t = 36 \, \text{cm} \)
- Refractive index of the glass slab, \( \mu_{\text{slab}} = \frac{3}{2} \)
- Refractive index of water, \( \mu_{\text{water}} = \frac{4}{3} \)

### Step 2: Substitute the values into the formula
We need to calculate \( \Delta x \):

\[ \Delta x = 36 \left(1 - \frac{\frac{4}{3}}{\frac{3}{2}}\right) \]

### Step 3: Simplify the fraction inside the parentheses
To simplify \( \frac{\frac{4}{3}}{\frac{3}{2}} \):

\[ \frac{\frac{4}{3}}{\frac{3}{2}} = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \]

### Step 4: Substitute back into the equation
Now substitute this back into the equation for shift:

\[ \Delta x = 36 \left(1 - \frac{8}{9}\right) \]

### Step 5: Calculate \( 1 - \frac{8}{9} \)
\[ 1 - \frac{8}{9} = \frac{1}{9} \]

### Step 6: Final calculation of the shift
Now substitute this value back into the equation:

\[ \Delta x = 36 \times \frac{1}{9} = 4 \, \text{cm} \]

### Conclusion
The shift produced in the position of the object is \( 4 \, \text{cm} \).

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