The lines in a grating are uniformly spaced at 1530 nm. Calculate the angular separation of the second order bright fringes between light of wavelength 600nm and 603.11nm. Answer in __mrad
To calculate the angular separation of the second order bright fringes, we need to use the formula:
sin(θ) = mλ / d
where:
- θ is the angular separation of the fringes,
- m is the order of the bright fringe (in this case, m = 2),
- λ is the wavelength of light,
- and d is the spacing between the lines in the grating.
First, we need to convert the wavelength of light from nanometers (nm) to meters (m). We have:
600 nm = 600 × 10^(-9) m
603.11 nm = 603.11 × 10^(-9) m
Now, we can plug in the values into the formula to calculate the angular separation for each wavelength:
θ1 = arcsin((2 × 600 × 10^(-9) m) / (1530 × 10^(-9) m))
θ2 = arcsin((2 × 603.11 × 10^(-9) m) / (1530 × 10^(-9) m))
Finally, we can calculate the angular separation between these two values:
Angular separation = θ2 - θ1
Now, let's calculate the angular separation in milliradians (mrad). To convert from radians to milliradians, we use the conversion factor: 1 radian = 1000 milliradians.
Angular separation (mrad) = (θ2 - θ1) × 1000
Plug in the values and calculate to find the answer in milliradians.