Given Information: Light of wavelength 631 nm passes through a diffraction grating having 485 lines/mm.

Part A: What is the total number of bright spots (indicating complete constructive interference) that will occur on a large distant screen?
*Answer: 7 (this is correct)

Part B: What is the angle of the bright spot farthest from the center?
*Answer: ???
-I am not sure what equation to use for this part of the problem....

Ooh wonderful! There is another problem similar to it...I am having trouble finding the # of fringes, but I think once I get help with that I can solve for the angle!!!

GIVEN: Light of wavelength 585 nm falls on a slit 6.66×10−2 mm wide.

Part A: On a very large distant screen, how many totally dark fringes (indicating complete cancellation) will there be, including both sides of the central bright spot?
*Answer: ?????

Part B: At what angle will the dark fringe that is most distant from the central bright fringe occur?
*Answer: I'm asuming that this will be the equation to use: d*sinA=(N+.5)*L

To find the angle of the bright spot farthest from the center, we can use the equation for the angular position of the bright fringes in a diffraction grating. The equation is given by:

sin(θ) = mλ / d

Where:
θ is the angular position of the bright fringe,
m is the order of the bright fringe (the number of bright spots away from the central bright spot),
λ is the wavelength of light, and
d is the spacing between adjacent lines on the diffraction grating.

In this problem, we have the following values:
Wavelength (λ) = 631 nm = 631 × 10⁻⁹ m
Spacing between adjacent lines (d) = 1 mm / 485 = 2.06 × 10⁻³ mm = 2.06 × 10⁻⁶ m
Order of the bright fringe (m) = 7 (since we want to find the bright spot farthest from the center)

Substituting these values into the equation, we get:

sin(θ) = (7 × 631 × 10⁻⁹) / (2.06 × 10⁻⁶)

Calculating this expression will give us the sine of the angle θ. We can then take the inverse sine (sin⁻¹) of that value to find the angle θ.

Let me calculate that for you.

To determine the angle of the bright spot farthest from the center, you can use the equation for the angle of diffraction for a diffraction grating. The equation is given by:

sinθ = mλ / d

Where:
- θ is the angle of diffraction
- m is the order of the bright spot (1, 2, 3, ...)
- λ is the wavelength of light
- d is the grating spacing (distance between adjacent lines)

In this case, the wavelength of light (λ) is given as 631 nm (or 631 x 10^(-9) meters) and the grating spacing (d) is given as 1 / 485 mm (or 2.05 x 10^(-3) meters).

To find the angle of the bright spot farthest from the center, you need to consider the case where m is the highest possible value, which means the brightest spot farthest from the center. In this case, m = 7, as given.

Substituting these values into the equation, we have:

sinθ = (7 * 631 x 10^(-9)) / (2.05 x 10^(-3))

Now, take the inverse sine (or arcsine) of both sides of the equation to solve for θ:

θ = arcsin((7 * 631 x 10^(-9)) / (2.05 x 10^(-3)))

Evaluating this expression using a calculator, you will find the angle (θ) of the bright spot farthest from the center.

There will be a bright spot wherever

d sin A = N *lambda,
where lambda is the wavelength, d is the line spacing, and N is an integer (including zero).

(1/485)*10^-3 m sin A = N*631*10^-9 m
sin A = N* 0.306

Allowed values of N are +/-1,2,3 and 0
So there are seven bright spots

B. The center of the pattern is n=0. Compute the angle for which N = + or - 3 and you will have the answer.