Question #43467

An LED is used as the monochromatic light source in a Young's Double Slit Experiment (YDSE) with a slit separation $d = 0.10 \text{ mm}$ and a screen placed at a distance $D = 1.0 \text{ m}$. Initially, the LED is forward biased with a current $I_1 = 10 \text{ mA}$. At this current, its junction temperature is $T_1 = 300 \text{ K}$ and it emits light corresponding exactly to its bandgap energy $E_g = 2.000 \text{ eV}$. When the forward current is increased to $I_2 = 50 \text{ mA}$, the junction temperature increases due to Joule heating. The thermal characteristics of the LED setup are such that the junction temperature rises at a constant rate of $1.0 \text{ K}$ per $\text{mA}$ of forward current increase above $10 \text{ mA}$. The bandgap energy of the LED material decreases with temperature at a rate $\frac{dE_g}{dT} = -4.0 \times 10^{-4} \text{ eV/K}$. Assuming the emission peak always corresponds to the bandgap energy, what is the magnitude of the shift in the position of the $10^{\text{th}}$ order bright fringe on the screen? (Take $hc = 1240 \text{ eV}\cdot\text{nm}$)