A laser emitting light of wavelength 580 nm is incident on a diffraction grating. What is the maximum number of lines per centimeter for which the m=5 principal maximum will be visible

To find the maximum number of lines per centimeter for which the m=5 principal maximum will be visible, we can utilize the equation for diffraction grating:

mλ = d(sinθ)

Where:
m is the order of the principal maximum
λ is the wavelength of the light
d is the distance between adjacent lines in the grating
θ is the angle of diffraction

Here, the wavelength of the light is given as 580 nm (or 580 x 10^-9 m), and we need to find the maximum number of lines per centimeter. So, we need to rewrite d in terms of lines per centimeter:

d = 1/(lines per centimeter) = 1/(L/cm) = 10 cm/L

To find the maximum number of lines per centimeter, we can substitute the given values into the equation for m=5:

mλ = d(sinθ)
5 x 580 x 10^-9 m = 10 cm/L x sinθ

Now, let's solve for θ:

sinθ = (5 x 580 x 10^-9 m) / (10 cm/L)
sinθ = 2.9 x 10^-8 rad/L

To find the largest angle using the sine function, we take the inverse sine:

θ = arcsin(2.9 x 10^-8 rad/L)

Therefore, the maximum number of lines per centimeter for which the m=5 principal maximum will be visible is given by the reciprocal of the angle in radians:

lines per centimeter = 1 / θ

Now, you can substitute the value of θ back into this equation to find the maximum number of lines per centimeter.

They should have specified an angle of incidence.

Assume the order number is m = 5 for a reflection angle of 90 degrees. Solve for the groove spacing.