In Young's double slits experiment, the position of 5th bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is :

Options

A. `12 mu m`
B. `60 mum`
C. `36 mum`
D. `48 mum`

Answer

To solve the problem of finding the separation between the slits in Young's double slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Position of the 5th bright fringe (x) = 5 cm = 5 × 10^(-2) m
- Distance between the slits and the screen (D) = 1 m
- Wavelength of light (λ) = 600 nm = 600 × 10^(-9) m
- Order of the bright fringe (n) = 5

2. **Use the Formula for Bright Fringes:**
The position of the nth bright fringe in Young's double slit experiment is given by the formula:
\[ x = \frac{n \lambda D}{d} \]
where:
- \( x \) = position of the bright fringe
- \( n \) = order of the bright fringe
- \( \lambda \) = wavelength of the light
- \( D \) = distance from the slits to the screen
- \( d \) = separation between the slits

3. **Rearranging the Formula:**
To find the separation between the slits (d), we can rearrange the formula:
\[ d = \frac{n \lambda D}{x} \]

4. **Substituting the Values:**
Substitute the values into the rearranged formula:
\[ d = \frac{5 \times (600 \times 10^{-9}) \times 1}{5 \times 10^{-2}} \]

5. **Simplifying the Equation:**
- The 5 in the numerator and denominator cancels out:
\[ d = \frac{600 \times 10^{-9} \times 1}{10^{-2}} = 600 \times 10^{-9} \times 10^{2} \]
- This simplifies to:
\[ d = 600 \times 10^{-7} = 6 \times 10^{-5} \text{ m} \]

6. **Converting to Micrometers:**
To express the answer in micrometers (1 m = 10^6 µm):
\[ d = 6 \times 10^{-5} \text{ m} = 60 \text{ µm} \]

### Final Answer:
The separation between the slits (d) is **60 µm**.

---