Å). The distance between the slits is 0.2 mm and the distance between the screen and the slits is 1.5 m. Calculate the wavelength of the sodium light.

In Young's double slit experiment, the formula to calculate the wavelength of light is given by:

λ = (d * sin(θ)) / m

Where:
λ is the wavelength of light
d is the distance between the slits
θ is the angle between the central bright fringe and the m-th bright fringe
m is the order of the fringe

In this case, we are given that 62 fringes are visible in the field of view with sodium light. The distance between the slits is 0.2 mm, and the distance between the screen and the slits is 1.5 m.

To calculate the wavelength of the sodium light, we need to find the value of θ for the given conditions. The angle θ can be calculated using the formula:

θ = tan^(-1)(y / L)

Where:
y is the distance between the central bright fringe and the m-th bright fringe
L is the distance between the screen and the slits

In this case, we are given that 62 fringes are visible in the field of view. Since the distance between the central bright fringe and the m-th bright fringe is equal to the distance between adjacent fringes, we can calculate the distance between adjacent fringes using the formula:

y = L * λ / d

Substituting the given values, we can calculate the distance between adjacent fringes:

y = (1.5 m * λ) / (0.2 mm)

Now, we can substitute this value of y into the equation for θ:

θ = tan^(-1)(((1.5 m * λ) / (0.2 mm)) / 62)

We can now substitute this value of θ into the equation to calculate the wavelength of the sodium light:

λ = (d * sin(θ)) / m

Substituting the given values, we can calculate the wavelength:

λ = (0.2 mm * sin(tan^(-1)(((1.5 m * λ) / (0.2 mm)) / 62))) / 62

This equation is not easily solvable algebraically, so we can use numerical methods or approximation techniques to find an estimate for the wavelength of the sodium light.