Single Slit Diffraction

This is a question related to single-slit diffraction. In single-slit diffraction, the angular width of the central maximum is given by the formula: where: - is the wavelength of the light, - is the width of the slit. Given: - The wavelength of the light is , - The width of the slit is . Substituting the values into the equation for : Next, the linear width of the central maximum on the screen is given by: where: - is the distance from the slit to the screen. Substituting the values: Thus, the linear width of the central maximum on the screen is . Therefore, the correct answer is (B) 1.28 mm.

For a single slit diffraction pattern, the angular width of the central maximum is given by: Where: - (wavelength of the light), - (width of the slit). Now calculate the angular spread of the central maximum: The total angular spread of the central maximum due to the single slit is approximately , i.e., Next, the angular width of a fringe in the double-slit diffraction pattern is given by: Where: - (slit separation). Now calculate the angular width of a fringe: The total number of fringes that can be accommodated within the total angular spread is:
Thus, the number of fringes that can be accommodated is 20.

In Young's double slit experiment, the shift in the interference fringes is due to the change in the effective wavelength of the light after passing through the glass plate. The new wavelength of light in the medium with refractive index is given by: where (wavelength in air), and (refractive index of the glass).
Thus, The number of fringes that shift due to the insertion of the glass plate is given by the formula: where is the thickness of the plate, is the change in wavelength, and is the wavelength of light. Since the thickness of the plate is , and the change in wavelength is: Substitute the values into the equation for fringe shift: Now, the number of fringes that shift is given by: where the fringe width , and is the distance between the slits and the screen, and is the separation between the slits. Since and are constant in this setup, the number of fringes shifted can be calculated. For the values given, the shift will be 100 fringes.