Calculate when a 3.0 mm thick, n as shown. the optical path length (OPL) for lig
ID: 1998894 • Letter: C
Question
Calculate when a 3.0 mm thick, n as shown. the optical path length (OPL) for light travelling from mirror 1 to mirror n = 1.54 piece of glass between the mirrors is oriented at theta = 0 and theta = 45. If the lights wavelength is 530 nm, how many wavelengths fit between the at each of the two angles? What is the free spectral range in each case. Explain how changing the angle of a piece of glass like this could be used to tune the wavelength of a single-mode laser? How would larger and smaller angles change the wavelength?Explanation / Answer
a) optical path length (OPL) = distance travelled in air + R.I times thickness of glass plate
= 17 x 10^-3 + 1.54 x 3 x 10^-3 = 2.162 x 10^-2 m in air
= 17 x 10^-3 + 1.54 x 3 x cos45 x 10^-3 = 1.809 x 10^-2 m
b) Wave length = 530 nm , d = 20 mm , for normal incidence m =( 2 xd )/ wave length = 75471 ie m can take values from 1 to 75471 , then the spectrum of wave lengths starts from 0.04 m to 530 nm.
when angle is 45 m = ( 2 x d x cos 45 ) / wave length = 53358 ; the spectrum of wave lengths is 0.02828 m to 530 nm.
c) By rotating the glass plate at a given angle , we can choose selectively a single wave length. This is due to the condition 2 x R.I x cos (theta) = mX wave length. Once Theta is known angle of incidence can be calculated. At that angle of incidence it allows only one walength and acts as a FILTER.
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