A diffraction grating gives a second-order maximum at as angle of 31�‹ for violet light (ƒÉ = 4.0 �~ 102 nm). If the diffraction grating is 1.0 cm in width, how many lines are on this diffraction grating?
Sorry about the double post, and
the question is:
A diffraction grating gives a second-order maximum at as angle of 31 degrees for violet light (wavelength = 4.0 x 102 nm). If the diffraction grating is 1.0 cm in width, how many lines are on this diffraction grating?
n lambda = d sin( theta )
d=n * lambda/sinTheta
solve for d. That is the distance between slits, so lines/distance= 1/d
change wavelength to cm if you want lines per cm
isn't that derived from the formula used for single slit though? and this is multiple slit (isn't that the same eqns as double slit?
so n= 2 (second order)
theta= 31 degrees
d= 0.1 m
lambda= 4.0 x 10^-7 m
(i'm required to solve in m)
is this correct?
no
To answer this question, we need to use the formula for diffraction grating:
d sin(θ) = mλ
Where:
d = spacing between the lines on the diffraction grating
θ = angle of diffraction
m = order of the maximum
λ = wavelength of light
In this case, we know the angle of diffraction (θ = 31°), the wavelength of violet light (λ = 4.0 × 10^2 nm or 4.0 × 10^-7 cm), and the order of the maximum (m = 2).
Rearranging the formula, we get:
d = (mλ) / sin(θ)
Now, substitute the known values into the formula and solve for d:
d = (2 × 4.0 × 10^-7 cm) / sin(31°)
Calculating this, we find that d is approximately 9.248 × 10^-7 cm.
To find the number of lines on the diffraction grating, we can use the formula:
Number of lines = Width of grating / Spacing between lines (d)
In this case, the width of the grating is given as 1.0 cm. Substituting the values, we have:
Number of lines = 1.0 cm / (9.248 × 10^-7 cm)
Evaluating this expression, we find that the number of lines on the diffraction grating is approximately 1.08 × 10^6 lines.
Therefore, there are approximately 1.08 × 10^6 lines on the diffraction grating.