The optical path of monochromatic light is the same if it goes through 2 cm of glass or x cm of ruby. If the refractiveTndex of glass is 1.510 and that of ruby is 1.760, then x is

Options

A. 1.716cm
B. 1.525cm
C. 2.716cm
D. 2.525cm

Explanation

To solve the problem, we need to use the concept of optical path length. The optical path length (OPL) is given by the formula:

\[ \text{OPL} = n \cdot d \]

where \( n \) is the refractive index of the medium and \( d \) is the thickness of the medium.

In this case, we have two different media: glass and ruby. The optical path lengths for both should be equal since the question states that the optical path of monochromatic light is the same if it goes through 2 cm of glass or \( x \) cm of ruby.

### Step-by-step Solution:

1. **Identify the given values:**
- Thickness of glass, \( d_1 = 2 \, \text{cm} \)
- Refractive index of glass, \( n_1 = 1.510 \)
- Refractive index of ruby, \( n_2 = 1.760 \)
- Thickness of ruby, \( d_2 = x \, \text{cm} \)

2. **Set up the equation for optical path lengths:**
Since the optical path lengths are equal, we can write:
\[ n_1 \cdot d_1 = n_2 \cdot d_2 \]

3. **Substitute the known values into the equation:**
\[ 1.510 \cdot 2 = 1.760 \cdot x \]

4. **Calculate the left-hand side:**
\[ 1.510 \cdot 2 = 3.020 \]

5. **Set up the equation to solve for \( x \):**
\[ 3.020 = 1.760 \cdot x \]

6. **Isolate \( x \):**
\[ x = \frac{3.020}{1.760} \]

7. **Calculate \( x \):**
\[ x \approx 1.716 \, \text{cm} \]

### Final Answer:
Thus, the value of \( x \) is approximately \( 1.716 \, \text{cm} \).