4. An antigen layer is being measured with a surface plasmon resonance (SPR) device. (a) Derive an equation for the sensitivity of the SPR device for an antigen layer with a thickness t at a distance d from the sensor surface. The sensitivity is dependent on the strength of the electric field. The sensitivity can be calculated by integrating the electric field equation of the evanescent wave with correct integration limits. Express the sensitivity as a sensitivity relative to the overall sensitivity. (b) The thickness is t = 6 nm and the penetration depth is dp = 320 nm. Solve the relative sensitivity when the antigen layer is i. directly on the sensor surface (d = 0), ii. on top of a layer of antibodies (d = 6 nm), and iii. at the penetration depth (d = dp). The relative sensitivity for the case ii is 0.0182