Question

Consider a diffraction grating of width 5 cm, with slits of width 0.0001 cm separated by a distance of 0.0002 cm. How many order would be observable at lemda = 5.5 x 10^-5 cm?

Answer 1

To determine the maximum observable order for a diffraction grating with a given wavelength, we use the equation n ≤ d/λ. With a slit separation of 0.0002 cm and a wavelength of 5.5 x 10^-5 cm, the maximum observable order is 3.

Step-by-step explanation:

The number of observable diffraction orders for a given grating and wavelength can be determined by the grating equation nλ = d sin θ, where n is the order number, λ is the wavelength, d is the slit separation, and θ is the diffraction angle. For the grating to produce the nth order maximum, the sine of the angle must be less than or equal to one since it's a physical limit of the sine function.

The maximum value of n for which this is possible can be found as n ≤ d/λ. Given a slit separation of 0.0002 cm and a wavelength of 5.5 x 10-5 cm, we can calculate the maximum order.

Using the formula we can rearrange it to n = d/λ and substituting in the numbers, we get:

n ≤ (0.0002 cm) / (5.5 x 10-5 cm)

n ≤ 3.63

Since the order number has to be an integer, the maximum observable order for this grating at the given wavelength is 3.