Final answer:
The nth-order diffraction angle for the shortest wavelength (380 nm) can be found using the equation ø = sin^(-1)(mλ/d), where d is the slit separation, m is the order of the diffraction maxima, and λ is the wavelength of light. To determine the change in the two angles if the distance between the screen and the grating is doubled, we can use the formula ø = tan^(-1)(D/L), where D is the distance between the screen and the grating, and L is the distance between the slits in the grating.
Step-by-step explanation:
The diffraction pattern produced by a diffraction grating can be determined using the equation d sin(Θ) = mλ, where d is the slit separation, Θ is the diffraction angle, m is the order of the diffraction maxima, and λ is the wavelength of light. In this case, the question asks for the nth-order diffraction angle for the shortest wavelength (380 nm). To find this angle, we can rearrange the equation to solve for Θ:
Θ = sin-1(mλ/d)
Plugging in the values given in the question, with m = n (since it is the nth-order diffraction angle) and λ = 380 nm = 3.80 x 10-7 m, we get the following:
Θ = sin-1((n⨯3.80 x 10-7)/1.2 x 10-5)
To find the change in the two angles if the distance between the screen and the grating is doubled, we can use the formula Θ = tan-1(D/L), where is the diffraction angle, is the distance between the screen and the grating, and L is the distance between the slits in the grating. Doubling the distance between the screen and the grating means doubling the value of D.
To determine the change in the two angles, we can calculate the new diffraction angle using the modified value of D and then subtract the original diffraction angle from it. This will give us the change in the angles.