Diffraction

In this YDSE setup, we are given the following parameters: - The distance between the slits is , - The distance between the slits and the screen is , - The wavelength of the light is , - The number of maxima observed inside the central maximum of single slit diffraction is 20. In a double-slit diffraction, the distance between adjacent maxima is given by the formula: where: - is the distance between adjacent maxima. For the single-slit diffraction, the angular width of the central maximum is given by: where is the width of each slit. The distance between adjacent minima in single-slit diffraction is: Now, we are told that 20 maxima of the double-slit diffraction lie within the central maxima of the single-slit diffraction. Therefore: Substituting the expressions for and : Simplifying this equation: Substitute : Thus, the width of each slit is . Therefore, the correct answer is (3) 2 μm.

Step 1: Understanding the Concept:
In Fraunhofer diffraction by a single slit, the position of the minimum on the screen is given by the condition . For small angles, the linear distance from the central maximum is .

Step 2: Key Formula or Approach:
1. Linear position of minimum: . 2. Linear separation .

Step 3: Detailed Explanation:
1. Position of the 1st minimum ( ): 2. Position of the 3rd minimum ( ): 3. Linear separation:

Step 4: Final Answer:
The linear separation is .