The maximum intensity in Young's double slit experiment is `I_(0)`. Distance between the slits is `d=2lamda`, where `lamda` is the wavelength of monochromatic light used in experiment. What will be the intensity of light in front of one of the slits on a screen at a distance `D=6d`?

Options

A. `(I_(0))/2`
B. `3/4I_(0)`
C. `I_(0)`
D. `(I_(0))/4`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the setup of the problem
In Young's double slit experiment, we have two slits separated by a distance \( d \) and we are given that \( d = 2\lambda \), where \( \lambda \) is the wavelength of the light used.

### Step 2: Identify the distance to the screen
The distance from the slits to the screen is given as \( D = 6d \). Since \( d = 2\lambda \), we can calculate \( D \):
\[ D = 6d = 6 \times 2\lambda = 12\lambda \]

### Step 3: Determine the position in front of one of the slits
The intensity at a point on the screen depends on the path difference between the light coming from the two slits. The point directly in front of one of the slits corresponds to a path difference of zero.

### Step 4: Calculate the path difference
In this case, since we are looking at a point directly in front of one of the slits, the path difference \( \Delta x \) will be:
\[ \Delta x = 0 \]

### Step 5: Calculate the phase difference
The phase difference \( \Delta \phi \) is related to the path difference by the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]
Since \( \Delta x = 0 \), we have:
\[ \Delta \phi = 0 \]

### Step 6: Use the intensity formula
The intensity \( I \) at any point on the screen in Young's double slit experiment can be expressed as:
\[ I = I_0 \cos^2\left(\frac{\Delta \phi}{2}\right) \]
Substituting \( \Delta \phi = 0 \):
\[ I = I_0 \cos^2(0) = I_0 \times 1 = I_0 \]

### Step 7: Conclusion
Thus, the intensity of light in front of one of the slits on the screen at a distance \( D = 6d \) is:
\[ I = I_0 \]

### Final Answer:
The intensity of light in front of one of the slits on the screen is \( I_0 \).

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