A slit ofWidth of ‘X’ is illuminated by monochromatic light of wavelength 650 nm at normal incidence.Calculate the value of ‘X’ for position of (i) first minimum at an angle of 300 and first maximumat an angle of diffraction of 300

To calculate the value of 'X' for the position of the first minimum at an angle of 300 and the first maximum at an angle of diffraction of 300, we can use the formula for the angular position of the minima and maxima in a single slit diffraction pattern.

For the first minimum, the formula is given by:

sin(θ) = m * λ / X

where θ is the angle of diffraction, m is the order of the minimum (in this case, m = 1), λ is the wavelength of the light, and X is the width of the slit.

For the first maximum, the formula is:

sin(θ) = (m + 1/2) * λ / X

where m is the order of the maximum (in this case, m = 1).

Given that the wavelength of the light is 650 nm and the angle of diffraction is 300, we can substitute these values into the formulas to solve for X.

For the first minimum:

sin(300) = 1 * 650 nm / X

Simplifying this equation, we have:

X = 1 * 650 nm / sin(300)

Similarly, for the first maximum:

sin(300) = (1 + 1/2) * 650 nm / X

Simplifying this equation, we have:

X = (1 + 1/2) * 650 nm / sin(300)

Now, we can calculate the value of X using a scientific calculator or trigonometric tables to find the sine of 300 degrees.

Please note that the final answer will depend on the units used for X.