In Young's double slit experiment carried out with light of wavelength `lamda=`5000 Å, the distance between the slits is 0.2 mm and screen is 2.0 m away from the slits. The central maximum is at n=0. the third maximum will be formed at a distance x (from the central maxima) equal to

Options

A. 0.5 cm
B. 1.67 cm
C. 1.5 cm
D. 5 cm

Explanation

To solve the problem of finding the distance of the third maximum from the central maximum in Young's double slit experiment, we can follow these steps:

### Step 1: Understand the parameters given
- Wavelength of light, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)
- Distance between the slits, \( d = 0.2 \, \text{mm} = 0.2 \times 10^{-3} \, \text{m} = 2 \times 10^{-4} \, \text{m} \)
- Distance from the slits to the screen, \( D = 2.0 \, \text{m} \)

### Step 2: Use the formula for the position of the m-th maximum
The position of the m-th maximum on the screen is given by the formula:
\[ x_m = \frac{m \lambda D}{d} \]
where:
- \( x_m \) is the distance from the central maximum to the m-th maximum,
- \( m \) is the order of the maximum (in this case, \( m = 3 \)),
- \( \lambda \) is the wavelength,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula for the third maximum (\( m = 3 \)):
\[ x_3 = \frac{3 \times (5 \times 10^{-7} \, \text{m}) \times (2 \, \text{m})}{2 \times 10^{-4} \, \text{m}} \]

### Step 4: Calculate the value
Calculating the above expression:
\[ x_3 = \frac{3 \times 5 \times 2 \times 10^{-7} \, \text{m}}{2 \times 10^{-4} \, \text{m}} = \frac{30 \times 10^{-7}}{2 \times 10^{-4}} = \frac{30}{2} \times 10^{-3} = 15 \times 10^{-3} \, \text{m} = 0.015 \, \text{m} \]

### Step 5: Convert to centimeters
To convert meters to centimeters:
\[ 0.015 \, \text{m} = 1.5 \, \text{cm} \]

### Final Answer
The distance \( x \) from the central maximum to the third maximum is:
\[ x = 1.5 \, \text{cm} \]

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