The grating equation for light diffraction states that for the diffraction pattern that forms when light is passed through an array of regularly spaced openings, that the diffraction order number (n) times the wavelength of the light (λ) is equal to the distance between slits (d) times the sine of the diffraction angle (λ), or:
Because the diffraction angle (θ) is difficult to measure, it is easier to mathematically derive it. If the diffraction pattern is projected onto a screen parallel to and a known distance, h, away from the diffracting grating, the distance from the zeroeth order to the nth order, xn can be measured (see figure 2). Because xn and h are perpendicular to each other, a right triangle is formed with the hypotenuse being the line formed from the diffraction source to the nth order line. Therefore, using trigonometry, θ is equal to the Tan-1 of xn divided by h, or:
Which when substituted into equation 1, gives us:
Figure 2: Mathematical derivation of angle (θ) of the 1st order diffraction by measurement of the distance from the 0th order to the 1st order lines (x1), and distance from the screen to the grating (h). Note that the lines form a right triangle, and hence trigonometry can be used to calculate θ.
The diffraction technique exploits the fact that coherent laser light constructively interferes with the normal skeletal muscle striation pattern formed by the interdigitation of actin and myosin contractile filaments. These striations, commonly referred to as skeletal muscle A-bands and I-bands behave as a diffraction grating to incident laser light (see Figure 3).
Figure 3: Orderly arrangement of A-bands (thick filaments) and I-bands (thin filaments) within the sarcomeric structure of myofilaments. Light diffracts through the I-band region of the muscle, and the spacing between I-bands is governed by sarcomere length.
Since the spacing of the I-bands is the same as the sarcomere length (since the Z-line is at the center of the I-band, and sarcomere length is from Z-line to Z-line), sarcomere length is then equivalent to d in the grating equation. Thus, given a laser beam of known wavelength, λ, a screen of known distance, h, from the muscle fibers, and a measurement of the distance between the 0th order to the nth diffraction order, xn, one can calculate sarcomere length (SL) with the following equation:
As one can infer from the equation, increases in sarcomere length would translate to closer distances between diffraction lines.
This technique is a useful tool to determine sarcomere length, both in vivo and in vitro. Examples of in vivo applications include the measurement of sarcomere length changes in fish while they are swimming and intraoperative sarcomere length measurements in humans during reconstructive procedures. Examples of in vitro applications are mechanical studies in which resting sarcomere length needs to be determined or controlled, and changes can be tracked while the muscle bundle or single fiber is activated. Knowledge of a fiber's sarcomere length is important to determine where you are on the length-tension curve and make sure the muscle is at a length which optimal for the tasks it needs to perform.who product specification who solution recipe for rehydration how many device can you have on netflix what science is on the act how many solution of linear equation how much business permit in quezon city why project management skills are important why design matters book where is the roadmap dealership in greenville roblox which tech company pays the most who owns positive solutions how much solution in contact lens case where is joma tech from how to buy a business location how many startup in india how much system in human body how much developing an app cost why equipment is important in harvesting crops who's are whose how solution is mixture who developed the triarchic theory of intelligence why system of a down how does roadmap work in jira how many products are made from corn where to manage amazon credit card when design thinking is relevant where to produce film where to set up a trust fund why business analytics how tech companies are valued how many device can use spotify premium who manufactured my windows which company makes monkeypox vaccine how workers compensation insurance works when solutions of kcl and pb no3 2 are mixed who manufacturers insulin differential equation whose solution is y cx c c 3 why solution of na2co3 is alkaline whose product is sql which project management certification is best who london video what company is bts under how many system restore points are kept roadmap when do shops open when product of inertia is zero where manager work where to buy clothes from manufacturer why startup india failed how company logos changed what design is on each oreo where is waste management from for support on mdm whom to connect how much tech trash for c4 where the solutions to the identified problems presented which company is worth the most why technology is good for society how to device unlock why technological change is important why solutions must be standardized where is saline solution in walmart what workers compensation where to get business casual clothes what are different types of design when technological singularity when a manufacturer saturated the market whose forest ncert solutions how much start up costs can be expensed whose forest ncert solutions what startup selection should i use why solution focused therapy is effective where to teach online whom definition why road map how to start online startup where to watch business proposal kdrama when startup menu when design takes flight how many tech startups fail how long project baseline results where project manager can work where to forecast weather why science is important for students how long system restore windows 10 roadmap when do restaurants open what technological development weegy which project management software is best why teaching is a good career doctor who equipment how many entrepreneurs in india how long system alcohol what business to start in 2022 what solution to use for window tint who set up a business how many engineering schools in the us where to study entrepreneurship where to teach spanish online how company equity works how much product to use skincare who product iphone what technology wants what product is good for hair growth when technological singularity how many development bank in nepal whose immune system is weakened why product management interview answer who's are whose why roadmaps fail which equipment is required for surgical hand asepsis whose product is dr pepper what two things must you check before using any equipment why development is important where to design clothes how far into the future does a solution roadmap forecast where to learn system design who science in 5 who workers compensation insurance where to manage storage on mac how much entrepreneur make a year