Monochromatic light from a helium-neon laser (wavelength=632.8 nm) shines at a right angle onto the surface of a diffraction grating that contains 130 960 lines/m. Find the angle at which one would observe the first-order maximum.
formula: (a+b)Sin theta = n wavelength
(a+b) = 1
____ m; n=1
wavelength=632.8*10^-9 m
=6.328*10^-7m
Sin theta=6.32^8 * 10^-7 * 130960
= 6.328*10^-7*130960*10^5
theta= 4.7536deg
= 4.75
is this done correctly?
130960
I don't know what a and b are supposed to be in your diffrection grating formula. The correct form of the quation is
d (sin i + sinr) = m*lambda
where i and r are the angles of incidence and reflection.
In your case sin i = 0, m = 1, and d is the grating line separation, which is your case is 1/(130960m^-1) = 7.636*10^-6 m.
Therefore
d sin r = 632.8*10^-9 m
sin r = 632.8*10^-9*130960 = 0.08287
r = 4.75 degrees
So you got the right answer, anyway
No, your calculations are not correct. Let's go through the calculations step by step.
Given:
Wavelength (λ) = 632.8 nm = 632.8 × 10^(-9) m
Number of lines per meter (N) = 130,960 lines/m
Order of maximum (n) = 1
To find the angle (θ) at which the first-order maximum occurs, we can use the formula:
(a + b)sinθ = nλ
In this case, a and b both equal 1 because we are considering the first-order maximum.
Substituting the values into the formula:
(1 + 1)sinθ = 1(632.8 × 10^(-9))
2sinθ = 632.8 × 10^(-9)
sinθ = (632.8 × 10^(-9)) / 2
sinθ = 316.4 × 10^(-9)
Now, we need to find the inverse sine (sin^(-1)) of this value to get the angle:
θ = sin^(-1)(316.4 × 10^(-9))
Using a scientific calculator:
θ ≈ 0.189 degrees (rounded to three decimal places)
Therefore, the angle at which one would observe the first-order maximum is approximately 0.189 degrees.